[Avodah] animal ownership

[Ben Waxman]

A relative asked me about neutering cats and I told him that I go by the 
"sell your animal to a non-Jew and have another non-Jew do the 
operation" psak.  This relative has some cats that he wants to neuter. 
He asked me what constitutes ownership. Meaning, my cat was born in my 
house, I take him to the vet, he sleeps inside, and has a name. My 
relatives cats are basically well fed street cats. He feeds them but 
doesn't give them shots, or let them inside, or take care of them in any 
other way.

Is ownership in this case a restriction? Does someone need to own a cat 
to do this operation? Is feeding a cat (that lives in your property) 
enough to constitute ownership?