Tight immigration restrictions were put into federal law in the 1920s, and as people born before that decade aged, they made up a smaller and smaller percentage of people in each state. The peak period of immigration to the United States, as a percentage of people who had already arrived, was about the turn of the century between the nineteenth and twentieth centuries. The Immigration and Nationality Act of 1965 loosened a lot of restrictions on immigration that formerly applied to whole regions of the world, resulting in a new increase in net immigration (but still not all the way back to historical peak levels).

One pattern that is long-lasting in these data is the extremely low rate of settlement of foreign-born persons in most states in the deep south (that is, the states of the old Confederacy). States that attracted more immigrants tended to be those that were more dynamic and with more personal freedom, and then the presence of immigrants in those states helped preserve the dynamism and personal freedom, setting up a virtuous cycle that attracted other immigrants.

Disclosure: my family background is one of ancestors who arrived in the United States well before the Ellis Island immigration station in New York harbor was even built, well in advance of the first major federal restriction on immigration, which was the Chinese Exclusion Act of 1882. My ancestors through whom I gain my family name arrived, father and son, after being born in New York state and then settling for a while in Wisconsin Territory, to Minnesota Territory sometime in the early 1850s. My wife, by contrast, is a first-generation immigrant herself, who first arrived in the United States in 1985.