For us, the prize money has always gone to the show bill for the horse. If it's more than the bill, then rider gets 15-25% or the owner keeps it (depending on how much money it is/what the contract says prior). However this is with the owner paying the show fees for a pro and possibly paying the trainer extra to ride in those classes. Junior catch riders generally earn no money, just the opportunity to show a horse without paying class fees.
Actually, junior riders can get paid these days. Years ago you'd get them a small gift. There is no USEF ban on juniors and $ now so in that situation, I'd talk to the parents or the trainer of the junior rider .
The barn I worked for it was 20% to the rider for classes over a certain amount; I forget what the cutoff was, but it basically meant the rider only got money for jumper classes or big hunter classics.
Traditionally, all money went to the owner. He also paid all the bills-- entries and the rider. Usually, the owner paid the rider a wage for riding, a negotiated percentage of winnings and might give him a tip as well.