You will need to get a transfer report signed by the person(s) listed as the owner(s) on the papers transferring the horse to you. Then you send the signed transfer and the original papers with the membership & transfer fee to the breed association.
If the system works anything like the system in the Uk then you need to get a transfer of ownership form from the society who issued the papers, then you need to fill the form in, get it signed by the last registered owner. Send the forms back to the society with appropriate (read extortionate) amount of money.
They will then Dither for 6 weeks before eventually sending back kthe papers in your name!
AQHA requires that all the transfers be made (basically so they can get the transfer fee & membership fee from each person inbetween) If you are lucky, (and don't mind breaking AQHA rules) and can track down the listed owner, ask them to sign a transfer directly to you. Then send in the papers as directed above.
Good luck. THe WPCS has had my papers for nearly 8 weeks! Very irritating as I can't move Reeco without the passport! I hope they come back fast as It will cost me £140 a week to keep him at the producers and he should be ready within the next 2 weeks!