As the manager of the McFatter One Name Study, my endeavor has been researching and making profiles for all the early McFatters and McPhatters (and their Georgian variant, McFather) possible. This is a rare surname, and all the American McFatters seem to stem from the same small area of Bladen and Robeson counties, North Carolina. However, the earliest generations of this family can be difficult to sort out.
See also: Part I and Part II, where I summarize the evidence as available to me then.
Recent developments: Duncan and Archibald (died 1831) were brothers, confirmed by Archibald's will! My theory is that Christian was their mother, with John as another brother; however, this is based on shaky onomastic grounds, as both John and Archibald named daughters Christian.
Duncan had no children, and Archibald's only son died in young adulthood. While Archibald surely has many descendants via his daughters, no McFatters or McPhatters descend from him or Duncan in the male line.
Next up, is William McFatter of Horry co. SC and (seemingly?) Decatur co. GA. I went into the details on this man here. Actually, there's two William McFatters who I suspect are the same man but can't prove it. William McFatter appears in 1820 Horry co. SC, and then twenty years later, a William McFatter appears in 1840 Decatur co. GA. This William married there in 1845 and then appears in 1850 with his wife Elizabeth and a young son, Kader.
Well, I think I found him in 1860 Terrell co. Georgia. William McPhatter, age 54, born SC, with four children: Alexander (is this "Kader" from 1850??), Catherine, Francis, and Nancy. If this is him, and it's hard to come up with another candidate, he's shaved about 12-15 years off his age.
Who are Daniel, J.B. and Sallie of 1870 Harris co. TX? Although indexed as McFatten, the entry for this family in the census looks to me like McFatter. Granted, lower case cursive S, R, and N can easily be mistaken for each other. If they are McFatters, then where are they in 1860?? Daniel's birthplace is given as Kentucky about 1796, since when did any McFatters live in KY??
What happened to Hugh and his family after 1840? Hugh McFatter, with his household including a boy under 5, a girl under 5, a woman aged 20-30 (presumably his wife) and a woman 60-70 (his mother or a mother-in-law?) are found in Columbus co. NC. This county lies between Robeson co. NC (the McFatter "Urheimat") and Horry co. SC, where as mentioned before, William McFatter was living in 1820. I can't find any trace of him or his family after 1840.
It is interesting that Daniel, the patriarch of the Randolph co. GA branch that adopted the spelling McFather, named a son Hugh. Daniel could not be a son of Hugh's, but perhaps a brother?