My aunt who is dying wants to give her house to her family. What is the best scenario to do to avoid paying any additional taxes?

Deed the property to the heirs -

The best scenario would have had to have been done years ago. Now any attempts to change ownership will be looked at as tax fraud.

A lot depends on the value of the house. Unless it's a multi-million dollar residence, the best method would be to will it to the heirs. Since there is a 2 million exemption from inheritance tax, the estate will owe no tax. The heirs would owe no tax until they sell it. And when they sell the only need to look at the change in value from the date of death. The only kicker to this is the cost of filing for probate.