Military Grad Ceremonies: What happens to the hats?

You know, when everyone all throws them up into the air at the same time. What happens afterward? Are they identifiable and returned? Does everyone keep a random one? Do they all get new ones?

My bet is that the owner’s name is in the hat on a tag somewhere. After the hat toss, pictures, etc, the owner finds the hat with his name on the label inside.

Wouldn’t graduating cadets get new caps along with their new ensign or lieutenant uniforms?

I believe it is tradition for all the children attending to rush out and retrieve them as souvenirs.