The Pentarchy (Five Patriarchal Sees) are:
EASTERN ROMAN (BYZANTINE) EMPIRE:
-Jerusalem (St. James)
-Alexandria (St. Mark)
-Antioch (St. Peter)
-Constantinople (St. Andrew)
WESTERN ROMAN EMPIRE:
-Rome (Sts. Peter and Paul)
Canon 6 of the Council of Nicaea (325) already spoke of special authority already exercised by Rome, Alexandria and Antioch, and Canon 7 approved the special honor given to Jerusalem, which as yet had no authority over other sees, not being even a metropolitan see:
- Let the ancient customs in Egypt, Libya and Pentapolis prevail, that the Bishop of Alexandria have jurisdiction in all these, since the like is customary for the Bishop of Rome also. Likewise in Antioch and the other provinces, let the Churches retain their privileges. And this is to be universally understood, that if any one be made bishop without the consent of the Metropolitan, the great Synod has declared that such a man ought not to be a bishop. If, however, two or three bishops shall from natural love of contradiction, oppose the common suffrage of the rest, it being reasonable and in accordance with the ecclesiastical law, then let the choice of the majority prevail.
7): Since custom and ancient tradition have prevailed that the Bishop of Aelia * should be honoured, let him, saving its due dignity to the Metropolis, have the next place of honour.*
The foundations of Constantinople, restructuring and enlarging the existing city of Byzantium, were laid after that Council, on 26 September 329 AD. This see was added, ranked second after Rome, in canon 3 of the Council of Constantinople (359) and canon 28 of the Council of Chalcedon (451), both of which decisions were rejected by Rome at the time:
…And the One Hundred and Fifty most religious Bishops, actuated by the same consideration, gave equal privileges to the most holy throne of New Rome, justly judging that the city which is honoured with the Sovereignty and the Senate, and enjoys equal privileges with the old imperial Rome, should in ecclesiastical matters also be magnified as she is, and rank next after her; so that, in the Pontic, the Asian, and the Thracian dioceses, the metropolitans only and such bishops also of the Dioceses aforesaid as are among the barbarians, should be ordained by the aforesaid most holy throne of the most holy Church of Constantinople; every metropolitan of the aforesaid dioceses, together with the bishops of his province, ordaining his own provincial bishops, as has been declared by the divine canons; but that, as has been above said, the metropolitans of the aforesaid Dioceses should be ordained by the archbishop of Constantinople, after the proper elections have been held according to custom and have been reported to him.
-Chalcedon, Canon 28
The Pentarchy was officially formulated in the legislation of the emperor Justinian I (527–565), especially in his Novella 131 and the theory received formal ecclesiastical sanction at the Council in Trullo aka the Quinisext Council (692), which was recognized by the Eastern Orthodox, but not by Catholics (the Pope protested and refused to sign the Canons since many of them exhibited an inimical attitude towards Churches not in accord with Constantinople, i.e. it condemned some practices then prevalent in the Latin Church. Justinian thus sent an army to force Pope Sergius to sign, but the imperial army at Ravenna came and marched to Rome in support of the Pope).
But even by 692 the Pentarchic system had been seriously disrupted. After the 7th century Arab conquests, and the Byzantine loss of the Rome-Ravenna corridor, only Constantinople remained securely within a state calling itself the “Roman Empire”, whereas Rome became independent, Jerusalem and Alexandria fell under Muslim rule, and Antioch was on the front lines of hundreds of years of recurring border warfare between the Byzantine Empire and the Arab Caliphate.
These historical-political changes, combined with the northward shift of the center of gravity of Christendom during the Middle Ages, and the fact that the majority of Christians in Egypt and Syria were Non-Chalcedonians who refused to recognize the authority of either Rome or Constantinople, meant that the original idea of five great co-operating centers of administration of the whole Christian church under the emperor grew ever more remote from practical reality.