@nabthefool Those are actually two different things when dealing with AKC.
Ownership, sole owner or co-own. I co-own all of my dogs with their breeders, so if anything happens to me they have something that shows they should get the animal back. Besides the breeder you could co-own with family members, friends, juniors, pretty much anyone. No limit for number of people that 'own' the animal in AKC that I know of (although there should be).
Registration - Full rights, Limited, Conditional, and others I think. Full rights is required to register litters of puppies from the animal, show in conformation, and probably a couple other things. Limited registration gives the registration for a pure bred dog but does not give the right to register litters/puppies with the AKC.
The first thing you probably need to do is find a breeder that will mentor you in titling a dog in showing. Once you have successfully accomplished that you would have made some contacts for someone to help with breeding.
Also let me point out that the ownership is NOT a legal owner, it is just for AKC paperwork. It does NOT give any legal rights to anyone but it does show the intention of sharing the property.