In Roman family law, the power that the male head of a family (paterfamilias) exercised over his descendants in the male line and over adopted children. Originally this power was absolute and included the power of life and death; a paterfamilias could acknowledge, banish, kill, or disown a child. He could free his male descendants from this obligation or turn over his daughter and all her inheritance to the power of her husband. By the end of the republic (from about the 1st century BC), a father could inflict only light punishment and his sons could keep what they earned.
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Potestas strongly contrasts with the power of the Senate and the prudents, a common way to refer to Roman jurists. While the magistrates had potestas, they had auctoritas. It's said that auctoritas is a manifestation of socially recognized knowledge, while potestas is a manifestation of socially recognized power. In Roman political theory, both were necessary to guide the res publica and they had to inform each other.
As the effective power of the Holy Roman Empire declined, kingdoms asserted their own independence. One way to do this was to claim that the king had, in his kingdom, the same power as the emperor in the empire, and so the king assumed the attributes of potestas.