Undocumented Immigrants Aren’t Who You Think They Are | FiveThirtyEight. This is a useful summary of undocumented immigrants to the U. S.
Illegal immigration from Asia is the fastest growing segment. However, many of these immigrants end up in debt bondage to the agents who get them into the country. The women often coerced into the sex trade.
There are an estimated 75,000 undocumented Canadians in the U. S. Conversely, U. S. citizens in the country illegally are the most frequently deported, although that was only 54 people in 2012.
There are no good estimates on the number of illegals in Canada. This is a summary of Canadian issues and notes that the numbers could be anywhere from 80,000 to 500,000.
Many of the more than 40,000 draft dodgers and deserters who came to Canada during the Vietnam war came as legitimate refugees. More than half stayed after the amnesty in the late 1970s (deserters can still be court martialed).
Then, of course, Canada was profoundly influenced by the British Empire Loyalists who moved to Canada during and after the Revolutionary war.