By the most liberal estimates, Russia now has about 15 million immigrants, but its immigration potential is far from exhausted. Ara Abramyan, president of the Union of Russian Armenians, said that in two decades Russia might have ten million Armenians, who would become one of the country's largest diasporas.
Of course, the mass migration now under way all over Russia gives rise to numerous problems. The country, which for several decades strictly regulated the travel of its own citizens, is not totally ready for this new reality. It is enough to say that no more than 20% of the 15 million immigrants reside in Russia legally.
The US has had a tradition of welcoming immigrants. I somehow expect this practice of illegal immigration is even less popular in Russia than the equivalent policies have been in the United States.