Yes , it is a gift since the EQUITY in the property transferred from your father to you
I imagine if we were to get technical, half the equity was a gift to you when your name was added to the title and the other half of the equity was a gift to you when his name was removed from the title
Note I am focused on the equity and not the value of the house or the debt so the “equity” could be different at the two points that the ownership was changed
But there is no “tax” on the gift just a reporting requirement on Form 709.... and if the equity transferred is less than $15000, then there is no reporting requirement either (and if the two steps occurred in two different years, then no reporting if the equity transfer was less than $30000)
