"Claim the house" basically means claiming itemized deductions for mortgage interest and real estate tax. There is nothing else about owning a house that would normally appear on your tax return.
If you don't pay the mortgage, you certainly don't claim a deduction for mortgage interest. The person who pays the mortgage gets the deduction.
You can deduct real estate tax for any house that you own, even if you don't live in it. So if you pay part or all of the real estate tax, you could claim a deduction for that (subject to the limit on the deduction for state and local taxes). But you can only claim the amount that you paid yourself.
