This was taken from UO Stratics. The Information is not being used to coherse dicisions or change what is in game currently, but to give ideas to Staff and Devs for later enhancment or changes to this great shard as they see fit.
http://uo.stratics.com/content/professions/taming/taming-pets.shtmlStabling Information
Leaving your pet in your house is not an option. It will lose loyalty rapidly once you are not in line of sight and once it is wild it will eventually vanish into thin air. So what to do with your pet while you don't need it or when you want to log out? The answer: stable it! To stable a pet say "stable", to get a pet from an NPC say "claim". The charge is 30 gold per pet each time you stable it.
If you say "Claim", the stablemaster will give you as many of your stabled pets as you currently have control slots available. If you say "claim [petname]", the stablemaster will give you the pet you specified if you have enough control slots available to control it. If you say "claim list" or specify a petname that does not match any of your stabled pets, you will get a list of pets that are currently stabled.
No matter where or on which facet you stabled your pet(s), you can claim them from any stablemaster.
People who are only friended to pets can not stable or claim them. You receive a message telling you "you don't own this pet" if you try to stable a pet you are friended to.
Pets that are fighting may no longer be stabled. You will get a message that "your pet seems to be busy".
A pet has to be "empty" in order for a stabemaster to accept it. ("You need to unload your pet.")
The number of pets a character can place on a stable master is based upon an average of 3 skills:
Taming, Veterinary, and Animal Lore.
If the total (adjusted value) of these 3 skills (Taming plus Veterinary plus Animal Lore) is
below 160, two pets may be stabled.
between 160 and 199.9, three pets may be stabled.
between 200 and 239.9, four pets may be stabled.
at or above 240, five pets may be stabled.
Additional stable slots are granted for reaching 100.0, 110.0 and 120.0 in Animal Taming, Animal Lore or Veterinary.
If you are mounted on a pet (ostard, llama, horse, nightmare, kirin, unicorn, ridgeback) you can safely log out on it.
The last paragraph is kind of veige and grey. I believe this was done to let GM's determine the number of slots after the initial 240 total skill points.