By 2050 (or the early 22nd century), I fully expect that the next great waves of immigrants would come from either sub-Saharan Africa [if the population recovers enough from the Red Plague (HIV-AIDS)] and/or the Middle East and North Africa. Those are the only parts of the world with growing populations that haven't yet made their imprint here.
Birth rates in the Middle East and particularly North Africa have crashed lately. In the Maghreb, they're below replacement levels, but population keeps going up because of the lag from the 1980s cohorts having children.
Saudi Arabia, Yemen, the Occupied Territories are the outliers for still having large families.