I am not a UT licensed attorney, and suggest you seek the advise of a UT licensed attorney that handles partition actions. Many of the appropriate answers to your inquiry require additional facts and information. For instance, who is on the note (promissory note with the bank), and the mortgage, and the title? Is there any equity in the real property? Who contributed to the equity and do you have agreement on the percentages contributed to the equity (through mortgage payments and/or down payment)? Is it in your interest for him to "buy you out" financially, and/or is it better for you to have him quit claim his interest and you refinance it yourself? These are the types of issues you should be prepared to discuss with a knowledgeable real estate lawyer in UT. There are others, though this would be a good start. If this answer was helpful, please indicate such. Good luck.
I agree with Mr. Bock and the information he points to would prove exceedingly helpful in answering you. If you bought the property in both of your names and you are both on the mortgage you should want out of that situation. In the case that neither of you qualify for a mortgage separately, you will have to look for a next best option.
If the property is in both of your names, there is little or no equity, and you want to own the home, all that would need to occur is a quit claim deed from him to you. That would cover your ownership. Ideally, you would write out a second document that states that you agree that the property has no equity and that he is giving you his interest in the property because he no longer wants the obligation.
If I were advising you regarding giving the property to him, I would insist that you make refinancing a condition of the agreement. You do not want to be left on the mortgage on a property owned by him. If he was unable to pay, the mortgage company could foreclose without even notifying you and then sue you for any money they lost in the process. This situation would be a serious problem for you.
Best of luck to you. I recommend that you take some time and consult with an attorney, even if you do not use their assistance in completing a transaction. You need an attorney to discuss the entirety of your situation with you.
Providing this answer does not form an attorney-client relationship. Most legal questions are exceedingly fact-sensitive and therefore this answer is a best-guess based on the information you provide. You should consult an attorney licensed in your state to further discuss your matter.