Mortgage: No one. To deduct the mortgage interest, the taxpayer must be obligated on the loan and actually make the payments. Since you make the payments but are not obligated on the loan, you can't deduct the interest. Your GF could deduct the interest if she paid the mortgage and you paid other household expenses to equalize things.
Property taxes: You. To deduct property property taxes, you must be an owner on the deed and actually make the payments. Your GF could deduct property taxes if she paid them.
HOA fees: Mostly non-deductible. The only part of HOA fees that would be deductible would be property taxes for common areas, but only if you have an itemized statement that specifically shows the property taxes. Then, the property tax deduction goes to the taxpayer who is both a property owner and actually pays the fee.
