What if you don't get into your zoned school

What happens if the school is overcrowded and a 5-year old doesn't get in? Who decides what other public school he would go to - the parents, the DOE, someone else? Also, does precise location within the zone matter? In other words, is someone right on the border more likely to be left out due to overcrowding, or is it pure chance? And does living on the border mean your "back-up" if you don't get in is the school whose zone you're bordering? We are looking at apartments in PS 199, and a couple are right on the border with PS 191 school zone, thus the questions... thanks.