It could be possible that not all schools use some kind of quill to keeo track of witches and wizards born in their country. What could some other ways be?
In the book I'm working on, there is no list at all. The seal on each acceptance letter is charmed to find a magical child who will be old enough to start school next, almost like a moth to a flame. Once the letter find someone, the child's name and all other information appear. The school keeps sending out bunches of letters until some just return back, letting them no there is no one else to recieve a letter. Muggle-born letters are sent two years before all the others with a tracking charm so a professor from the school can follow it.
But what are some other methods the rest of you have come up with?