Wrong again:
The autocephalacy of Cyprus was confirmed (against Antioch) at the Ecumenical Council of Ephesus, without any schism, c. viii:
Our brother bishop Rheginus, the beloved of God, and his fellow beloved of God bishops, Zeno and Evagrius, of the Province of Cyprus, have reported to us an innovation which has been introduced contrary to the ecclesiastical constitutions and the Canons of the Holy Apostles, and which touches the liberties of all. Wherefore, since injuries affecting all require the more attention, as they cause the greater damage, and particularly when they are transgressions of an ancient custom; and since those excellent men, who have petitioned the Synod, have told us in writing and by word of mouth that the Bishop of Antioch has in this way held ordinations in Cyprus; therefore the Rulers of the holy churches in Cyprus shall enjoy, without dispute or injury, according to the Canons of the blessed Fathers and ancient custom, the right of performing for themselves the ordination of their excellent Bishops. The same rule shall be observed in the other dioceses and provinces everywhere, so that none of the God beloved Bishops shall assume control of any province which has not heretofore, from the very beginning, been under his own hand or that of his predecessors. But if any one has violently taken and subjected [a Province], he shall give it up; lest the Canons of the Fathers be transgressed; or the vanities of worldly honour be brought in under pretext of sacred office; or we lose, without knowing it, little by little, the liberty which Our Lord Jesus Christ, the Deliverer of all men, hath given us by his own Blood.
Wherefore, this holy and ecumenical Synod has decreed that in every province the rights which heretofore, from the beginning, have belonged to it, shall be preserved to it, according to the old prevailing custom, unchanged and uninjured: every Metropolitan having permission to take, for his own security, a copy of these acts. And if any one shall bring forward a rule contrary to what is here determined, this holy and ecumenical Synod unanimously decrees that it shall be of no effect.
ccel.org/ccel/schaff/npnf214.x.xvi.xii.html
And of course, Rome, Alexandria and Antioch were set up at Nicea c. vi, without schism:
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.
ccel.org/ccel/schaff/npnf214.vii.vi.viii.html
The same with Jerusalem:
The most magnificent and glorious judges said:…The arrangement arrived at through the agreement of the most holy Maximus, the bishop of the city of Antioch, and of the most holy Juvenal, the bishop of Jerusalem, as the attestation of each of them declares, shall remain firm for ever, through our decree and the sentence of the holy synod; to wit, that the most holy bishop Maximus, or rather the most holy church of Antioch, shall have under **its own jurisdiction **the two Phœnicias and Arabia; but the most holy Juvenal, bishop of Jerusalem, or rather the most holy Church which is under him, shall have
under his own power the three Palestines, all imperial pragmatics and letters and penalties being done away according to the bidding of our most sacred and pious prince.
ccel.org/ccel/schaff/npnf214.xi.xv.html