How do I and what are the costs of adding my name to a property fully paid off in a defacto and a non defacto situation? :o

Huh. What does "defacto" have to do with anything?

To get your name added to a property, the property owner has to issue a deed (usually a quit claim deed) from the current ownership to the new ownership.

This deed is then filed with the county. You can do it by yourself at minimal cost or you can get a title company (recommended) to do it usually for a few hundred dollars.

If the property is not paid off and there is a lien on it, then you can't issue such a deed without permission of the lien holder.