The information in this answer is general information and is not intended as legal advice, nor do I intend to create an attorney-client relationship with any reader by answering this question or otherwise contributing as a member of Trulia.com.
Thanks for the question.
There are a couple of terms that it seems might be applicable - including "adverse possession."
That being said, this IS a legal issue and the only way for you to be certain that you are getting the best legal advice is to speak with a real estate attorney.
Give us a call at 312.242.1000 if you would like the name of a great real estate attorney.
We are more than happy to help!
Best of luck to you.
Americorp Real Estate
Brokers Associate, e-PRO