A “Testator” is someone who makes a will.  A person who has a will, when they die, is said to have died “testate”, i.e., with a will.  Someone who dies without a will dies “intestate”.  Each state has a set of laws, consisting of both statutes and judge-made law (court rulings), that determine what happens to the property and debts of someone who dies ‘intestate’.  Generally speaking these laws are fairly inflexible, and those left behind must follow them regardless of what the person who has died ‘really wanted’.