1. is the owner your spouse?
Adding another owner who is not the spouse of the current owner might incur transfer tax. For example NYC collect 1% city transfer tax and NY state collect 0.4-0.65% of state transfer tax for unrelated owners.
2. does the house have mortgage?
While federal law permits transfer between spouse and children when the house has a mortgage, it is best to check with the bank before such transfer.
3. Usually a quitclaim deed is sufficient, transfer the title from owner X to owner X+Y.