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Intestate refers to a situation where a person dies without leaving a valid will. This status has significant legal implications because, in the absence of a will, the distribution of the deceased's estate is determined according to state law, specifically following the intestacy statutes. These laws outline how assets are divided among the surviving relatives, which can vary significantly from what the deceased might have chosen if they had created a will.

The other choices pertain to different legal concepts: leaving behind a will signifies dying testate; legal adoption does not impact intestacy; and incompetency relates to an individual’s capacity to manage affairs, not directly to the absence of a will. Understanding the term intestate is crucial for navigating the legal landscape of estate management and inheritance.