Legal Question in Family Law in Utah

I would need more information to be able to fully answer your question. If you owned the house free and clear of any mortgage debt before the marriage, then you would be entitled to the house without her having any interest. However, if you borrowed money to buy the house and made mortgage payments during the marriage, then she may be entitled to some portion of the equity. The fact that the house is titled just in your name makes no difference.

Probably not. The house is considered marital property. If you have no pre-marital agreements to the contrary the best she could seek would be part of any increase in equity. Over the past three years houses have declined as a rule, so there would not be any increase in equity.