homeownership and divorce

I bought a duplex in my name and put my mother on the deed as a joint tenant with full rights of survivorship. She has no financial obligation and has been living in it, paying rent with my stepdad for several years. The mortgage is in my name only. I bought this home many years after she married my step-dad. She is afraid he will have legal rights to the home and so is waiting to serve him with divorce papers until we know what we should do. We live in Oklahoma. My mother wants to put the house in my name only and sign a quitclaim deed. My stepdad has been very manipulative and gained access to my mothers assets in the past and now she is almost penniless. Obviously this factors heavily into the reason for the divorce. Will he have any legal claim to a house my mother owned during their marriage? She is not selling her share to me. She simply wants it out of her name. We have no legal contract between my stepdad and my mother and me concerning this house. No agreements as to what might be done in case of divorce or death have ever been discussed with my stepdad.