The 'mystery' branches where there seem to be no Gidley descendants in the male line in the UK (please let me know if I'm wrong!) are as follows: (there are of course many descendants in the female line)
1) The descendants of George Gidley born about 1802 in Bovey Tracey, Devon. He married Sarah Colman and moved first to Dover, then to Poplar.
2) The descendants of John Gidley of Brixham, Devon and his wife Hannah Earle, who married in 1789. He was a trawlerman, and like many of his trade, as times grew hard in Brixham John and his family moved firstly to Ramsgate, Kent, then to Hull, Yorkshire, and finally settled in Grimsby, where they prospered, as probate records show. One son emigrated to Australia, and there may well be Gidleys from this line there.
3) The Gidleys of Chudleigh. A confusing tree, whose members are difficult to track at present. Some are descended from George Gidley and Susanna Brookland who married in Zeal Monachorum in 1724. One particular family based in Chudleigh moved first to Bishopsteignton, Devon, then emigrated to Australia, where there are many descendants. The settlement examination of Joseph Gidley in 1833 is transcribed here, to show the difficulties in tracking this particular Gidley of Chudleigh:
'The examinant was born in Chudleigh, and informed by his father that he (his father) was born at Bow, near Crediton, and when young he worked with his father at Whiteway in Chudleigh, where his father lived as a gardener, and continued to work with his father in the gardens at Chudleigh until about the age of 10, when he went to Bristol and worked by the week on the nursery grounds of Miller and Sweet about 12 months. Then he went to Dawlish and agreed to work for Sir William Watson to work in his gardens at 7/- a week wages, and after he had worked there about a year and a half went into the house of Sir William Watson and had his meat and drink there, but slept out of the house and his wages continued at 7/- a week and that he had worked and had his meat and drink in the house about 3 years.
The examinant and his master had some words and Sir William Watson gave him a month's notice to leave the service and quitted at the end of the month, then agreed with Lady Paulett for 25 guineas a year wages and lived with her ladyship about 8 months, then went to Mount Edgecombe and agreed with the Head Gardener at 10/6 a week wages and lodged at the Garden House and continued there about 2 years when he got married at Stoke Church and further saith that he has done no other act to gain a settlement.' The decision went against Joseph, and the Chudleigh churchwardens and overseers were requested to deliver him and his wife out of Chudleigh to Dawlish, which was considered to be his legal settlement.
4) The Gidleys of Deptford, Kent. Another confusing tree, involving more than one family, who may or may not be linked. Two heads of families were Thames lightermen, and there is a possibility that their surname was actually Gridley. John Gidley baptised in 1785 in Deptford was the son of George Gidley and his wife Sarah. It is presumed that this is the same John Gidley who was bound as an apprentice waterman to Edward Farrell in Deptford in 1804, gaining his freedom in 1814. Having examined the baptismal affidavit books for watermen at the Guildhall, I see that John's baptism was vouched for by a fellow waterman, usually a close relative. No trace of any earlier Gidleys can be found in the watermen's records, but there is certainly a William Gridley, who was baptised at St Olave's, Southwark, in 1770, and who was the son of another William Gridley, waterman, baptised 18 February 1746 in Welnetham, Suffolk.
5) Two small branches living in York and Islington in the 19th century and descended from John Gidley and Mary Maria Treweeke who married in Stoke Damerel in 1815. It is looking increasingly likely that this branch links to the Ashreigney part of the Winkleigh family.
6) There are also some isolated, small trees of families in Plymouth.
7) Gidleys in London in the 19th century are still not all allocated to trees yet.

Emigration
It was noticeable, though, I suppose, fairly obvious, that many of those Gidleys who emigrated or who just moved long distances in this country were illegitimate, or had step-parents. It was also fairly common for the husband to emigrate first, and be joined some years later by the rest of his family.

Gidley family history in the USA.
There are now far more Gidleys in the USA than there are in the UK. Thanks are owed to my distant Gidley cousin Carol Gertner, whose generosity has allowed me to build a preliminary picture of the Gidleys in America. No doubt there is more to be discovered.
By 1850 they were in the following states:
1) Massachusetts.
The earliest Gidley family known to be in Massachusetts was that of Henry Gidley, his wife Joan, and their children born in Boston 1663 - 1670. The large family of Gidleys in Dartmouth and New Bedford, Massachusetts, all seem to descend from Henry's son, Hezekiah. Possibly another and quite different family are the descendants of Content Gidley (whose origins are still uncertain) through her son, William, who married Phebe Mosher in New York state. The offspring of this particular couple spread over the USA in a remarkable manner, and none remained in the Eastern US by the third generation.
Roughly contemporary, but in Newport, Rhode Island, was John Gidley b. ca. 1671 in London, and part of the Winkleigh branch of Gidleys. A complete pedigree of John's descendants was known to exist in about 1920, but now seems lost, and by the 1850 census there do not seem to be any Gidleys in the male line traceable to him. Nor can I at present link John with Henry Gidley in Boston.

2) New York State.
Jasper Mauduit Gidley from the Honiton part of the Winkleigh branch also went to America. Described in his father's will as 'my unhappy son', he fought against the British in the American War of Independence. He was in Albany County in 1800, and left 5 sons, of whom at least three moved on to Michigan, where they founded families. Other sons remained in New York State, and left many descendants.
Some of the New York Gidleys were descendants of the Massachusetts family of Content Gidley. They had settled in Saratoga County by the end of the 18th century, and many were known to be Quakers. They quite quickly spread further west to the Mid West, and then on across the Rocky Mountains to Oregon, Washington State and California. The move to the Black Hills of South Dakota led to James Williams Gidley's career as a distinguished palaeontologist.
3) Virginia.
In 1769 a John Gidley was transported to Virginia for stealing a bale of cloth in the Crediton area of Devon. It is not yet known which family he belongs to. At first it was thought he must be the John Gidley born ca. 1735 from the Spreyton part of the Winkleigh branch, who was married to Mary Blanchard (a co-defendant in John's trial was a Blanchard), but this John is known to have fathered a son in 1773 in South Tawton, Devon. A tantalising reference in the parish register entry for this baby's christening mentions 'the father having been transported', but this probably refers to John's documented removal back to Spreyton in 1772 under the Poor Law settlement arrangements. By 1790 either John the Transportee or his son John had moved to Kent County, Maryland, and then later to Monongalia County, now in West Virginia.
4) Alabama.
The story goes that James Gidley born 1796 of the Buckfastleigh part of the South Devon branch stowed away on a ship to America in about 1815, was shipwrecked, rescued, and carried to South Carolina. By 1850 he and his large family were living in Benton County, Alabama. By the end of the 19th century the meat trade had taken at least one branch to Texas.
5) Illinois.
Descendants of the New York branch of the Massachusetts family.
6) Indiana.
a) Miami County. Descendants of John, transported to Virginia.
b) Porter County. John Gidley of the Dean Prior part of the South Devon branch, his wife Mary (nee Maddick) and his son John.
7) Maryland.
In Baltimore in 1850 there was a Gidley family whose race was given as black. They are possibly associated with John the Transportee (or his son John), whose census entry in Maryland in 1820 lists 2 coloured males.
8) Ohio.
a) Morrow County. Descendants of the New York part of the Massachusetts Gidleys.
b) Washington County. Descendants of John the Transportee.
9) Pennsylvania and 10) Virginia.
Also descendants of John the Transportee.

Ten years later in 1860 even more states had Gidley families, or more familes had arrived from different origins:
11) California.
Gidleys from Cornwall, attracted by the mining. William S Gidley's origins in England are uncertain but he is the right age to belong to the Cornish Gidleys, with the S commemorating his mother's surname of Simmons.
12) Illinois.
Descendants of Samuel Gidley and his wife Susanna Mann, from Buckfastleigh, are enumerated in Rock Island County.
13) and 14) Iowa and Michigan.
More descendants of the New York Gidleys.
15) Missouri.
a) Caldwell County. Descendants of John the Transportee.
b) Sainte Genevieve. The German Guethle family from Baden in Germany, some of whom anglicised their name to Gidley.
16) Ohio.
The existing Gidleys were increased in Lucas County by Richard and Dinah Gidley and their family from the Winkleigh branch, and in Cuyahoga County by William and Sarah Gidley from the Dean Prior branch.
17) Wisconsin.
More Gidleys from Cornwall, who came to extract the lead in Mineral Point, in common with many other Cornish families. One son, Richard, fought in the 2nd Wisconsin Infantry in several battles of the American Civil War, and claimed to have fired the first shot from the infantry at the Battle of Gettysburg, although this is completely unsubstantiated by any military expert.

After 1860
More families arrived, including James Gidley and his wife Christiana, who emigrated to Orleans County, New York State, with their family in about 1867. He was descended from the Dean Prior Gidleys of South Devon, as was another arrival, Edwin Gidley who emigrated to Philadelphia in 1868, and was joined by his wife and family in 1874. The textile mills in Lawrence, Massachusetts, attracted Gidleys working in the woollen industry in Buckfastleigh, including three brothers who emigrated in the 1890s. One is the ancestor of Pamela Gidley, film star and actress in the USA.
In Michigan John Gidley married Ellen M Kellum in Jackson County in 1866 and founded a family. He was born in England in about 1843, but it is not certain to which family he belongs. It is looking likely that he is one of the Winkleigh Gidleys, possibly a son of Richard Gidley and his wife Dinah Herbert from Throwleigh, Devon, who emigrated to Ohio, USA, with most of their family between 1851 and 1860.

Gidley family history in Canada
Canada attracted fewer Gidleys than the USA, they tended to emigrate at a later date, and many of those that did start off in Canada subsequently moved over the border to settle in America.
To date I have found 7 families who emigrated to Canada.
1) Thomas Gidley of the Ashreigney part of the Winkleigh branch. Born in Plymouth in 1804 he moved first to London, and in 1833 was possibly the carpenter found not guilty at the Old Bailey of housebreaking. In 1843 he and his 5 sons emigrated to Ontario, and settled in Huron County where he became a respected citizen and JP. Some of his descendants later moved on to the US.
2) Some members of the Egg Buckland branch of the South Devon family emigrated to Canada where they were found on Prince Edward Island in the 1881 and 1891 censuses. Other members of that family emigrated firstly to Canada in 1856, then in 1871 onwards to Saunders County, Nebraska, USA. Several family members from both branches seem to have gone further westwards to British Columbia.
3) John Gidley, sometimes known as John Gundry Gidley, of the Gidleys of Cornwall, emigrated between 1851 - 1854 to the Great Lakes area. He spent time in both Canada and the upper peninsula of Michigan, USA, before finally settling in Penetanguishene, Ontario, on Georgian Bay. He was described on his death in 1893 as 'Captain John Gidley, boat builder and mariner, who pioneered the development of Canadian watercraft'. His descendant Bryan Gidley runs the Gidley Family website and the Gidley DNA testing project (see link below).
4) John Gidley, a blacksmith from Dittisham, and part of the South Devon Gidleys, emigrated with his large family to the Hamilton area of Ontario in 1871. Again, some of the family later moved to the USA.
5) Bartholomew Gidley of the Winkleigh branch, born in Chagford in 1845 and a tailor by profession, had emigrated to Canada by 1872. He brought up his family in Westminster, Ontario.
6) Frederick Henry Gidley born in Poplar, London, and descended from the South Devon Gidleys, probably emigrated to Canada in 1868. By 1900 he and his wife were in Westminster, Ontario, and a possible son was in Chicago, moving later to New York.
7) One of the Chudleigh Gidleys, Hubert John W Gidley, died in 1913 in Vancouver.

Gidley family history in Australia
Australia is a difficult country to research, because of the government's policy of destroying all personal details from the censuses. Consequently, all I have to date can be summed up as follows:
1) In 1821 two men, William Gidley and George Gidley, listed consecutively, so possibly related, were listed in convict gangs issued with rations in Sydney. It is not known who they were, or what became of them.
2) John Gidley, who married Elizabeth Facey in Chudleigh in 1819, followed, with the rest of his family, his oldest daughter Mary Ann Gitsham and her family who had emigrated to Australia in 1849. John's origins are not known. He was possibly from Chudleigh, or possibly from Bovey Tracey. He died in 1884 in Kangaroo Flat, Victoria. Some of his family moved to Adelaide, South Australia.
3) Hubert Gidley, one of the Chudleigh family, and born in Great Torrington in 1820, emigrated, probably to Victoria, in the early 1850s. There were several letters waiting for him in the 1860s which were indexed in the uncollected letters index from that state. His family left behind in Bishopsteignton, Devon, were left destitute, and don't seem to have joined him in Australia.
4) James Gidley and his wife Susan, one of the Winkleigh branch, and born in Christow, Devon, in 1840 emigrated with their 2 sons in 1878-9 to Auckland, NZ, where a daughter Ellen was born in 1885, then moved on again in 1889 to Lithgow, New South Wales to work for Sir John Hay in Sydney.
5) Three Gidley seamen decided to settle in Australia. The first was one of my own line, Albert Frederick William Gidley, born 1867 in Southampton, Hants., who emigrated in the 1890s to New South Wales, and married there.
6) The second seaman was Herbert Samuel Gidley, born in Grimsby, Lincs., in 1873. He also married in New South Wales in the 1890s, and settled there.
7) The third seaman was again from my line, John Martin Gidley, who sailed from Plymouth with his wife and two daughters in 1911.
There will no doubt be others.

Gidley family history in New Zealand
A Henry Gidley, whose origins are not yet known, was awarded a grant of land from the Crown Lands Office in Auckland in 1870. Hannah Gidley died in 1892 aged 63, and again her origins are unknown. Most of the other Gidleys that I know to have emigrated to New Zealand (apart from James and Susan Gidley whose brief stay is mentioned above in the Australia paragraph) were from the Winkleigh branch. The 2 youngest sons of Gustavus Gidley, solicitor of Plymouth, and from the senior Winkleigh line, emigrated in the 1870s - 1880s to South Island, where they were buried in 1913 and 1946 respectively. One son of Northleigh, the elder son of Gustavus, was killed in France in 1918. The younger son, William Gustavus, left descendants on South Island. Robert, the younger son of Gustavus, and who was described as a gardener at his burial, had 2 daughters.
Another of the Winkleigh branch, Richard Hamlyn Gidley of Whitchurch, Devon, died in Wellington, New Zealand in 1913, where his will was proved.
Leonard Arthur James Gidley, a seaman from Poplar, but whose family originated in Buckfastleigh, married in New Zealand in 1920.