If the paper collar doesn't promote a response from his owner you will want to pop him down the vet to see if he's chipped - he may in fact be reported lost? If he is chipped and not reported missing, and the owner is in your area (vet won't give you details of his true owner, data protection I believe) you might want to start positive deterrant action (squirty water bottle whenever he arrives).
I've taken three strays in, all of which were clearly street cats, unchipped, un-neutered and very much worse for wear, so I think maybe your visitor is a lonely pet cat with access issues at home (no cat flap, likes to be outdoors when Mum goes to work). His Mum probably hasn't the first idea he's playing away from home.
To test him, take up your resident cat's food whilst you're not in attendance so Visitor never gets to eat at yours, and you'll soon see the reason for his constant attendance. If he's in for the cuddles and warmth, and he's not chipped, then it is quite possible he's looking for a new home, but still being fed by his real Mum.
If he's obviously hungry, pop a permanent safety collar on him with a tag containing your phone number and resume feeding. Post flyers in local shops, libraries and vets and register him on National Pet Registers "Found" listing with a photo. There is a legal requirement to take reasonable steps to locate a stray cat's owner. Advertise any found, unregistered (tattooed/chipped) cat for a minimum period, I think it's seven days in England, before you can claim ownership.
The real owner should be determined to contact you if she feels he is about to disappear from her life forever.
One of my fosters is finding our home a challenge, he was a long term city stray who had no qualms about testing out various homes for himself (which was how he ended up in rescue, after one of his temp Mummys discovered him in her house with a broken leg) but despite being neutered, chipped and fostered to me 3 years ago, Theo is still actively seeking a new home in the area, behaving very much the way your visitor is doing, as basically Theo would prefer to be an Only cat.
Even though he's chipped (and we have a microchip controlled catflap) I frequently put an ID collar on Theo when I suspect he has a new
victim Mummy (his lack of appetite and rare appearance is the giveaway), and from this I've discovered he has been almost adopted twice (by concerned folk who explain they thought he'd been abandoned and believed me to be a bad Mummy
- eek) and has been taken to the vet more often than this (he still has the limp from his old injuries and plays this up for attention outside the school gates - he really is very convincing).
My vet says there's almost nothing I can do, (other than keep him as an indoor cat and if you met Theo you'd understand this is quite against nature for him) Theo is hard headed and stubborn, currently residing in my outdoor kennel but within earshot of the fridge door.
One day he will worm his way into someone's heart and home (he is magnificent and very friendly when it suits him) and I may never see him again.
Sadly this will mean he won't get his pain meds (he feels the cold in that leg and if he knocks it, his limp worsens) and the insurance I have for him will not be in place for the next time his delicately repaired cruciate ligament gives way, he ends up at a new vet and that leg has to come off. When I explain his physicality to these good folk who he woos so easily, that he really is a huge commitment, which will only get bigger as the years go on. They're off like a shot and he's suddenly my lovely boy again.
http://www.catchat.org/lost.html#found
