Alaska is breaking new ground as the first state to authorize a court to render a custody order for pets. This is link to the statute:
http://www.legis.state.ak.us/PDF/29/Bills/HB0147A.PDF
An Alaskan Court may now in a divorce action make orders as to, “if an animal is owned, for the ownership or joint ownership of the animal, considering the well being of the animal.”
The law in Texas is still that a pet is property and is awarded as such. Despite this, I have had my share of property disputes about pets that were pet custody cases in disguise, and no less intense then those involving children.