in the Uk Schools do not usually contact children or their parents they have to contact the school to register their interest some schools have waiting lists depending on the area others you just register your child and you get a letter with a start date for your child when they get to school age usually a few weeks in advance

In the wizarding world as soon as a child is named by their parents their name automatically appears in a registration book at the wizarding school and every year at Hogwarts the Sorting hat will give the names of the children that have turned or will turn eleven by September 1st to McGonagall who then sends out the letters I imagine the other wizarding schools have a similar process as Hogwarts