Talk to an attorney who knows tax laws. There are issues regarding gift taxes, basis, maintenance, liability, mortgage insurane, etc. Your bank will tell you how to have your friend assume the mortgage. Note: Your friend can't assume 1/2 the mortgage. S/he will add his/her name to the mortgage and you will both be liable for the entire mortgage.
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.