"Large numbers of them emigrated to the United States, and are the most important population element in Appalachia and other areas such as the Ohio Valley and the Ozarks. They are an important element in Texas and Oklahoma as well."
The first group came in five ships in 1718, arriving at Boston. They dispersed, and some settled a town in New Hampshire called Londonderry.
My Ulster Scot ancestors then moved to Falmouth, Maine. This family later misgrated to Canada, Minnesota, and the pacific northwest, among other places.
British and Ulster Scots immigrants who arrived in the mid and late 19th Century and early 20th Century were rapidly absorbed into the English Puritan descended (or Yankee in the original sense) population. Hillary Rodham may seem to be an arch-Yankee, but is, on her father's side, the granddaughter of late 19th Century Welsh and English immigrants to the coal fields of Pennsylvania.
Per Allen Eckman's "The Frontiersman"