The cliche understanding is that dogs mark their territory with pee. At times I’ve been on walks with family and friends with half a dozen dogs. There have been occasions where they form a line just to pee in the same spot.
So how does the ownership work? Is it like a co-op? Last one to pee wins?
If I’m not mistaken, it’s just to say where the dog has been.
As far as pee ownership goes, if you can get to the pee first, it’s yours. You should probably ask the owner first if it’s not a stray.