In California, "Adverse possession" requires a lot: You have to occupy a place continuously for 5 years, like how an owner would. You have to pay all taxes on the land for that time. You have to be clearly occupying the land, so it's obvious to all (including the owner). You have to be acting like you are the owner of the land: Getting & paying for electric, water, internet, trash pickup, etc..
So, there's a high bar that has to be met.
I don't know what would happen if I owned a piece of property that I didn't live on, and both I and the adverse posessor tried to pay. Maybe they'd take both payments? Maybe it's a race condition? No idea.
Maybe there's a legal mechanism for carving off a piece of a larger property that you've been "openly and notoriously" squatting for the requisite amount of time. If so, you'd pay the tax bill post facto.
But... I don't really know anything, let alone cross-jurisdictionally. Those are educated guesses.