[gizmo686]

Public schooling in the US is done at a very local level, so varies significantly across the country. Where I grew up, the 1 school in your district was required to accept you. However, some of the nearby districts would let you apply to them, and accept people on a case by case basis. For the most part, this let academically strong students go anywhere; but was also used to let families who move stay at the same school (including siblings who were not yet enrolled).

There are also charter school, which are a weird mix between public and private schools, that typically operate on a mix of applications and lotteries. Plus private schools that can enroll pretty much whoever they want.