Hello and thank you for using Just Answer. Purchasing a home with your mother does not create a tax liability for either you or your mother.
Living with and taking care of your parents is not a taxable gift to your parents. Your mother paying the balance of the home is not a taxable gift to you. If you sell the home and you received your mother share of the sale of the home that would be a taxable gift and your mother must report the gift, (net profit over $13,000 in 2009), on her tax return.