Yes, immigrants obviously can and do adapt to their host culture and it happens often, perhaps most of the time (I don't know of stats on that). But what cause

Yes, immigrants obviously can and do adapt to their host culture and it happens often, perhaps most of the time (I don't know of stats on that). But what causes this, and what's the "absorption rate"? With no migration controls at all, could such absorption be overwhelmed and cease working?