Go 3 ways on a mansion

Q: If i want to buy a mansion and split the payments with 2 other people but, the house will be in my name who will own the house once its paid for

A: If you purchase the property & have it in your name (only) then the others who ’share ‘ it with you would be (in a way) making rental payments for using it. Unless you have something else worked out in writing with all the parties signing the agreement, you would own the place as well as have any tax benefits, liability issues, insurance obligations, maintenance, etc.