Puss

We seem to have acquired a cat.
It's not a stray, as it seems to be in too good a condition. It was being thrown out of another student house opposite from us and followed my housemate in last night. It then stayed for the rest of the evening untill I put it out at 11.30.
He (It's definitely a he, which has confused us even more, if he's a pet why's he not been done?) is beautifully behaved. Last night he just feel asleep at the bottom of my bed, then decided after a couple of hours he wanted a cuddle. He hasn't made a mess anywhere, doesn't beg excessively, hasn't scratched either of us, and is just such a gentleman.
This morning he appeared again, and is now fast asleep on my bed again. We've been quite naughty and fed him, and I'm now feeling faintly guilty, what if he is someones pet, and they're worried about him?
One of my cats at home left us for a short while for a neighbour, as we were mean and wouldn't let her sleep on the beds at night. A neighbour however would let her upstairs at night, and spoilt her rotten with food. The only thing making me feel better about the situation is I did put him out last night, so he could have one home (if he has one) if he wanted to.

Should we carry on letting him in, and feeding him? It's so tempting, I really miss having a cat!