Legally, this depends on where you live.
The law in Denmark now states that ownership of cat only exists if the cat is chipped. Anyone taking in a stray cat should have the cat checked - if it is chipped, they may not keep the cat, but they or the vet, doing the checking, is obliged to contact the owner the cat is registered to. If that person no longer wants the cat, is able to keep it, or has died and no relatives are prepared to keep the cat, it can then be re-registered to the person who has take it in.
If the cat was not chipped, the finder may pay to have this done, and the cat can then not be claimed by anyone else, or put down by muncipal animal control, or by a person who dislikes cats and find it on their property.
I suspect this last group of people are not bothered by the fact that they should check if the cat is chipped or not.
Emotionally, it depends on your relationship to your cats, whether you "own" them or not. I talk to mine, and they respond with a variety of sounds or through body language.
They own me to the extent of being huffy if I am away too long in the course of the day, or have the temerity to go away for an overnight stay anywhere - we have not yet progressed to (perish the thought!) a holiday.
And when they want a cuddle, they expect me to drop whatever I am doing and oblige!
18 months after his death, they still occasionally look for my husband in his work-shop or stare at the empty sofa.
So who owns whom?