I don't even see it as marking territory or ownership since that isn't what they are doing.

They're communicating with other dogs when they sniff and pee; so I look at it like scrolling social media. They're just on PissBook. When they sniff, they're reading. When they pee, they're commenting. When they take a dump, they're literally shitposting.

Not a dog scientist, but I remeber listening to an npr seqment from an actual dog scientist. I believe that cliche is a misconception. Dogs don't pee around areas to mark territory. If that were the case, they would be peeing all over your house to mark it as theirs. Rather dogs pee to leave their scent as a "Hello! Mr. Fluffy Butt was here."

I have always thought of it as how graffiti taggers work. They are always tagging over each other's work. The last one to paint gets the most exposure but you can still see remnants of more recent taggers the lay under the topmost. Eventually the oldest stuff just gets covered completely. They don't necessarily pick their canvas because there is other work they try to cover up, they pick their canvas for the location and exposure.

I know it's always described as "marking their territory," but it always seems more like saying "I was here" to me. Our dogs for sure consider our house and yard their territory. If someone comes to the door or into the yard, they bark like crazy, and have a protective stance. They aren't at all like that when I take them for walks. They're happy to meet other people and other dogs, and they aren't at all upset when they smell other dogs' pee.

I think it's more like exchanging business cards.

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.

So it’s more like a dog guest book, got it. Does anyone know why they pee where they pee? My dog picks a particular spot in the bushes at my parent’s house and he does it without fail every time.

And my male dog pees on the same spot as my female dog. What up with that?

Dogs don't enforce territorial ownership so the pee is mostly just "I was here". Anxious dogs might pee in inappropriate areas as a way to feel safer. In wolves the markings are more serious. They will enforce their territory so its more of a "leave or we'll kill you" kind of thing.

My grandparents had a dog that when we brought our dog, would follow our dog around to all the spots ours peed on after the car ride, sometimes peeing before and after on a spot with our dog peeing there in between.

It's not really ownership, per se. It's really more like planting a flag to say "I was here". They're leaving their scent behind to let other outsider dogs know that they are around the area, like a calling card. Sometimes the pheromones in the urine can let other dogs know if they are in estrus, so it has a useful social/mating component to it.