This office was originated from Near East (Eastern Roman Empire, widely known as the Byzantine Empire). 

It is also similar to Biblical judges, who are not to be confused with modern legal judges, since the word refers to leaders who took charge of the affairs of the tribes in case of war, and who assumed leadership of their respective tribes in the succeeding times of peace. In accordance with the needs of the time, their functions were primarily martial and judicial.

Giudicati were Sardinian medieval autochthonous regions which existed from about 900 AD. Originally they were Byzantine districts that became independent during the Arab war against Byzantium. Their governors were the Iudikes (it.: Giudici), elected by the Corona de Logu (Parliament). 

Translation of German terms

Translation German -> English
I do not know the correspondent English word for "Erbrichter"; a possible translation is "Judge" (?), an administrative officer (equivalent to head of the village or of an administrative district), with the possibility to inherit his position to one of his sons or to sell it. 
As far as the word "Erbgericht" is concerned, the English translation may be Administrative Jurisdiction (or District). 

Translation German -> Italian
The Italian word for "Erbgericht" is Giudicato and for "Erbrichter" is Giudice.