U.S.A
The Skillmans in the U.S.A. believe that one Thomas Skillman arrived with the British Expedition to take New Amsterdam (now New York) in 1664 and that a great many of them are descended from this one man. Thomas is a common Skillman name but I have only found one likely Thomas, on record, of the right age at that time. He was son of Richard and Rose of Littlemore near Oxford who was baptized 3 Aug 1639. There is another possible choice and that is Thomas son of Thomas and Alice of Oving in Buckinghamshire who was baptized 22 Oct 1626 and would have been at least 37 at the time. The pioneering Thomas apparently married in the Long Island area and thereafter led a very full life which is documented. I see there are hundreds of Skillmans in the U.S.A. now, some of which I have contacted.
Australia
I know of two who emigrated permanently to Australia and have Skillman descendants there. Firstly, there was Henry and his wife Hannah (nee Brooks) who arrived in 1850. He was from London but his branch originated in Deddington, Oxfordshire. He died in Booral, N.S.W. Secondly, there was Henry born in Harpenden, Hertfordshire in 1862. He arrived as a single man in about 1880 and had two marriages, the second being with Elizabeth Clarke. He died in Cairns, Queensland.
Initially, I was greatly helped by work done by my aunt Ann Skillman. My own research has been at County Records Offices, using Mormon records, talking to elderly relatives and often receiving documents from them, and writing to all and sundry. Recently I have also used the Internet with great success. I have over 2800 names of family, cousins and in-laws on record now, and a study full of papers and pictures.
I can, with reasonable certainty, trace my line back to Roger of Hynton-by-Brackley, Oxfordshire who died in 1560. I supply members of the family with their section of the tree, if asked, but the tree as a whole is enormous and does not exist as a single entity. The blame for this falls mainly on the large Victorian families. Earlier families were much smaller. Regrettably, my "twig" is probably going to die out. Our only son has two daughters.
There is an ongoing Skillman DNA comparison project that you can study at
http://www.familytreedna.com/public/skillmandnaproject/
(this page updated on 7Dec2010)