what authority does the head of the church have?
Papacy, the jurisdiction of the episcopal see
Pope
 papacy, the jurisdiction of the episcopal see is called the Holy See. 
what was the structure of the roman catholic church based on UNANSWERABLE who is the head of this church? Pope do they have a holy city? Yes, Vatican City in which country is this in? Italy
wiki:25673353
Pope [SEP] Introduction
The current pope is Francis, who was elected on 13 March 2013, succeeding Benedict XVI. While his office is called the papacy, the jurisdiction of the episcopal see is called the Holy See. It is the Holy See that is the sovereign entity by international law headquartered in the distinctively independent Vatican City State, established by the Lateran Treaty in 1929 between Italy and the Holy See to ensure its temporal, diplomatic, and spiritual independence. The Holy See is recognized by its adherence at various levels to international organization and by means of its diplomatic relations and political accords with many independent states.