I’ve always understood that St. Peter and his successors in the See of Rome hold primacy of both honour and authority over all the other bishops of the World.
The following pertains to the Pope’s authority over Eastern Catholic Patriarchs and Metropolitans, etc. …
From the Decrees of Vatican I …
Wherefore we teach and declare that, by divine ordinance, the Roman church possesses a pre-eminence of ordinary power over every other church, and that this jurisdictional power of the Roman pontiff is both episcopal and immediate.
Both clergy and faithful, of whatever rite and dignity, both singly and collectively, are bound to submit to this power by the duty of hierarchical subordination and true obedience, and this not only in matters concerning faith and morals, but also in those which regard the discipline and government of the church throughout the world.
In this way, by unity with the Roman pontiff in communion and in profession of the same faith , the church of Christ becomes one flock under one supreme shepherd [50] .
This is the teaching of the catholic truth, and no one can depart from it without endangering his faith and salvation.
From the Code of Canons for the Eastern and Oriental Churches (Promulgated on their behalf by the Holy Ecumenical Pontiff, the Pope of Rome) …
TITLE III. THE SUPREME AUTHORITY OF THE CHURCH
Canon 42 - Just as, by the Lord’s decision, Saint Peter and the other Apostles constitute one college, so in a similar way the Roman Pontiff, successor of Peter, and the bishops, successors of the Apostles, are joined together.
Chapter I. The Roman Pontiff
Canon 43 - The bishop of the Church of Rome, in whom resides the office (munus) given in special way by the Lord to Peter, first of the Apostles and to be transmitted to his successors, is head of the college of bishops, the Vicar of Christ and Pastor of the entire Church on earth; therefore, in virtue of his office (munus) he enjoys supreme, full, immediate and universal ordinary power in the Church which he can always freely exercise.
Canon 44 - §1. The Roman Pontiff obtains full and supreme power in the Church by means of legitimate election accepted by him together with episcopal consecration; therefore, one who is already a bishop obtains this same power from the moment he accepts his election to the pontificate, but if the one elected lacks the episcopal character, he is to be ordained a bishop immediately.
§2. If it should happen that the Roman Pontiff resigns his office (munus), it is required for validity that he makes the resignation freely and that it be duly manifested, but not that it be accepted by anyone.
Canon 45 - §1. The Roman Pontiff, by virtue of his office (munus), not only has power over the entire Church but also possesses a primacy of ordinary power over all the eparchies and groupings of them by which the proper, ordinary and immediate power which bishops possess in the eparchy entrusted to their care is both strengthened and safeguarded.
§2. The Roman Pontiff, in fulfilling the office (munus) of the supreme pastor of the Church is always united in communion with the other bishops and with the entire Church; however, he has the right, according to the needs of the Church, to determine the manner, either personal or collegial, of exercising this function.
§3. There is neither appeal nor recourse against a sentence or decree of the Roman Pontiff.
Canon 46 - §1. In exercising his office (munus) the Roman Pontiff is assisted by the bishops who aid him in various ways and among these is the synod of bishops; moreover the cardinals, the Roman curia, pontifical legates and other persons and various institutes assist him according to the needs of the times; all these persons and institutes carry out the task committed to them in his name and by his authority for the good of all the Churches, according to the norm of law established by the Roman Pontiff himself.
§2. The participation of patriarchs and other hierarchs who preside over Churches sui iuris in the synod of bishops is regulated by special norms established by the Roman Pontiff.
Canon 47 - When the Roman see is vacant or entirely impeded nothing is to be innovated in the governance of the entire Church; however, special laws enacted for those circumstances are to be observed.
Canon 48 - In this Code the term “Apostolic See” or “Holy See” applies not only to the Roman Pontiff but also, unless it is otherwise prescribed by the law or the nature of the matter indicates otherwise, dicasteries and other institutes of the Roman curia.
This should probably be a sticky.
… how does the authority of the Pope over regular bishops compare to his authority over Patriarchs (ex. Patriarch of Antioch or Pope of Alexandria)? And how does the authority of patriarchs compare to that of other bishops?
If the question is about Orthodox Patriarchs, that is a question for the non-Catholic religions forum.
