So hypothetically, one could own a share of a share of a company depending on the contract?

Is there a minimum right? Granted co-owners can't exercise full rights of ownership. Is there a minimum right that cannot be partitioned between legal persons?

So I own my phone more than you own my phone when there is greater chance that a local court will rule that I own my phone?

My issue is with the concept of partial ownership. It makes no sense to me. Do the legal definitions occasionally apply to a co-owner and occasionally not apply to a co-owner? Or rather, the legal definitions hold absolutely but rather pertain to a more abstract interpretation of the original property?

Convention. It's like the alphabet. The alphabet isn't required to be in ABC ordering by a fundamental force of nature but rather just some particular ordering for better communication.