Hogwarts registration deadline clarification?

I was always curious whether the actual deadline for registering at Hogwarts was July 31st or if it just goes by the prospective student's birthday. Harry kind of screwed that up for us. They both make sense I guess, although with all those students it should take more than JUST the month of August to finalize the roster, right? There are cancellations, late sign-ups, all those 'unforeseen circumstances' things. I'm okay with the obligatory "it's magic, dude" comments :)