What phrase refers to the process where an heir legally inherits property upon the death of an ancestor who did not leave a will?

The phrase that refers to the process where an heir legally inherits property upon the death of an ancestor who did not leave a will is "intestate succession." In situations of intestate succession, the laws of the state or jurisdiction determine how the deceased's assets are distributed among their surviving relatives, according to a predefined hierarchy. This legal framework ensures that the estate is fairly allocated based on familial relationships, typically prioritizing spouses, children, and other direct descendants.

In contrast, testate succession occurs when a person dies leaving a valid will, indicating their wishes for asset distribution. Expectancy succession is not a recognized legal term related to inheritance processes, and probate succession is more about the legal process of validating a will and administering the estate rather than the specific circumstances under which assets are inherited when no will exists. Thus, intestate succession is the correct concept for the situation described in the question.