Final answer:
A government ruled by a system where authority is transmitted from relatives to relatives is known as a monarchy, which can be either ceremonial or hold actual power, often including forms of patrimonialism.
Step-by-step explanation:
When a state or country is ruled by a government in which the system of power involves the transmission of authority from relatives to other relatives, it is known as a monarchy. This form of government is characterized by a single individual, known as a monarch, who rules until he or she either dies or abdicates the throne. The rights to the title are usually claimed through hereditary succession or sometimes as a result of divine appointment. While the monarchies of some modern nations might be seen as ceremonial, with the royals acting as figureheads, the tradition of aristocratic families inheriting power remains.
Historically, forms of patrimonialism also exhibited familial power transmission, where the ruler's administration and military were personally appointed by the master, with no rights of their own. Systems such as the political organization of ancient Egypt, where the royal decree compelled the construction of pyramids, exemplify this form of monarchy.