My father left his house in a trust with me as his sole trustee. I am currently letting my sister live there, rent-free. Her-live-in boyfriend pays most of the utilities. After she dies, will he have any advverse possessions rights(squatter right)? Is there anything I should do to to protect myself because I intend to take the house back and administer the house myself. Thanks!

No , not really, what you should do, and maybe already have done is have a rental agreement signed by your sister and her boyfriend, following your state law ( they may need to pay 1 dollar rent or something in some areas) That way it proves they are renters for court. Also after she dies, he will still be on the month to month rent, so all you would have to do is give him the 30 to 60 day notice to move out..
It just makes it easier to have all of the agreement in writing.

Heck tell them it is for their protection if you would die.