what law do they follow?
Canon law
Catholic Church
Canon law () is the system of laws and legal principles made and enforced by the hierarchical authorities of the Catholic Church to regulate its external organization and government and to order and direct the activities of Catholics toward the mission of the church.
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 what authority does the head of the church have? Papacy, the jurisdiction of the episcopal see what is his real name? The current pope is Francis, who was elected on 13 March 2013, succeeding Benedict XVI. who are the other members of this church? Ordained clergy, bishops,  priests, non-ordained ministers, lay missionaries, lay ecclesial ministers.
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Catholic Church [SEP] Canon law
Canon law () is the system of laws and legal principles made and enforced by the hierarchical authorities of the Catholic Church to regulate its external organization and government and to order and direct the activities of Catholics toward the mission of the church. The canon law of the Latin Church was the first modern Western legal system and is the oldest continuously functioning legal system in the West, while the distinctive traditions of Oriental canon law govern the 23 Eastern Catholic particular churches "sui iuris." Positive ecclesiastical laws, based directly or indirectly upon immutable divine law or natural law, derive formal authority in the case of universal laws from promulgation by the supreme legislator—the Supreme Pontiff—who possesses the totality of legislative, executive and judicial power in his person, while particular laws derive formal authority from promulgation by a legislator inferior to the supreme legislator, whether an ordinary or a delegated legislator.