Yes you can claim ownership by adverse possession but that would only be necessary if there was some question as to the authority of the agent to act for the owner. If there is some question, you would file an action to quiet title based on the combination of your record ownership and adverse possession.

That will work however the various companies would be considered affiliates of one another under US corporate law because they are under common control. However, you could do as you indicate in your post.

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