Catholic Theocracy is an ideology that seeks to value and preserve the Catholic faith and traditions and uphold them into law, rejecting anything that contradicts the faith and keeping the state close and loyal to the Church.
The head of the Catholic Church is the Pope, or also called the Bishop of Rome, who is elected by the College of Cardinals most of the time. When the Pope is elected, he stays in the papacy until he dies or resigns, but resignation is very rare case. The Cardinals are appointed by the Pope, who also chooses who are the next electors in the next conclave (Papal election), Cardinals voting over the age of 80 is restricted.
Like the Cardinals, a Secretary for Relations with States, who is responsible for international relations, is also appointed by the 
Pope.
The Catholic Theocracy's legal system also has fullness of legislative, executive and judicial powers, which is rooted in the canon law.
History
Work In Progress
In the Bible, specifically Matthew 16:18-19, Jesus has said to his Apostle, Peter, "That thou art Peter; and upon this rock I will build my church, and the gates of hell shall not prevail against it. And I will give to thee the keys of the kingdom of heaven. And whatsoever thou shalt bind upon earth, it shall be bound also in heaven: and whatsoever thou shalt loose upon earth, it shall be loosed also in heaven". Appointing him as the first Bishop of Rome, or Pope, and his Apostolic succession has continued to this day.
In the year 313 AD, Roman Emperors Constantine I and Licinius issued the Edict of Milan, which ended Christian persecution in the Empire but did not make Christianity the official state religion, that was 67 years later when Emperor Theodosius I issued the Edict of Thessalonica.
During and after the fall of the Roman Empire, the Germanic barbarians who weakened the empire converted to Christianity to ally with the religious ones in the regions they were invading, which split the Roman Empire into two: the Western Roman Empire, who's loyal to the Bishop of Rome, and the Eastern Roman Empire, who's loyal to the Patriarch of Constantinople, which then split communion in 1054.