There are some old notes in my files from some 1998 RootsWeb submissions on this Alexander Adair, indicating he was born in County Antrim, Ireland "before 1750" as was his wife Mary Anne "Mollie" who may have been born a Steele.They appear to have come directly to South Carolina.They arrived in South Carolina on 28 May 1767, presumably "right off the ship."The arrival is listed in the South Carolina Council Journal #33, pp 150-157, among Protestants having arrived:Mary Adair, Alex'dr Adair, James Adair, Margaret Adair.
Apparently there is a book "Misc. Adair Families found in GA, MS, AL" by Shirley Brown Adair (which I haven't seen) that lists the children of Alexander as John, Jean, Benjamin, "Tobithis" (Tabitha?), and Robert who married one Hannah Prather.(James and Margaret Adair who arrived with Alexander and Mary could have been a brother and sister-in-law to Alexander, but the relationship is not stated.)From what you write there was a daughter Anna, and it sounds like she may have married Hannah's brother.Perhaps you have a more complete outline of this family than what I was able to cobble together from my notes.
Also, around 1785-86, Alexander fathered an illegitimate son named Stephen by a woman named Ann McClure.(Alexander was fined in court for bastardy.)Ann later married one Francis Braddock and it appears that Stephen used the surname Braddock.
Some of these Adairs went to Tippah County, Mississippi as did Stephen Braddock and his family.
Robert Adair went to Graham County, Mississippi in 1840.Had children Robert, John, Benjamin, Mary, Bazell, Lucienda, Ruth, and William.The name "Holloway" was carried down to Robert's grandson by his son Bazell, who named a son Brice Holloway Adair.
So far as I know I am not related to this particular Adair line (although all these Southern Adairs might have been related to one another in one fashion or another).If you contact RootsWeb archives you can probably find more correspondence on this line.Good luck to you.If what I have written is redundant stuff you already know, please accept my apologies.I'm sorry but I have little more information than what is written here.