Inheritance
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Inheritance is the practice of passing on property, titles, debts, and duties when someone dies. Those things usually go to family members. Inheritance has been very important in human society for a long time.
If only sons and other male family members get the inheritance, it is called patrilineal succession. If only daughters and other female family members get the inheritance, it is called matrilineal succession.
Cultural inheritance is called legacy. Genetic inheritance is called heredity.
The person who gets the property and other things when someone dies is called the heir (male) or heiress (female).