In iirc 8th grade, I've placed high in the final round of a Moscow-wide physics competition, incidentally hosted by MSU. My classmate, who placed even higher, and myself have received an invitation to enroll in the MSU-affiliated maths/physics focused school (#2, the schools in Moscow are all numbered semi arbitrarily). As far as I recall, every time I'd go to one of those competitions bulk of the people in later rounds were from #2 and #57, another math-focused school. The kids from other schools who did well were, I assume, largely scooped up by those targeted schools.

EDIT: Oh, and the maths/physics/etc. competitions started at neighborhood level, so every school would typically send at least a few kids, and encourage the kids who were better at the subjects to do well. I went to neighborhood biology/history/etc. competitions too, but never did very well. I assume whoever did well in those and went into next rounds could go on to enroll into a different set of specialized schools :) Also, some parents did enroll their kids straight into those schools, but I dunno how prevalent that is. They are very ability focused, unlike US private schools that I've heard of where money and helicopter parenting seem to be a major factor.

As a side note, my friend did enroll into #2, and I didn't go because was too lazy to commute 40mins one way when my own school was a 3-minute walk (it was a subway trip for him as is, so I'd like to think that was the difference ;)). We've both done well for ourselves but he's definitely much better at math now.