Here are the results of some research I have done on the Eastern Church of Rome. Please tell me if I am wrong on some areas.
When an Eastern patriarch dies, the Roman Curia appoints a Vicar Apostolic Patriarchal (which corresponds to a Vicar Capitular in the West), who summons a council to elect a new patriarch. The Vicar Apostolic presides over the council and hands the Patriarchal Dikanikion to the man elected patriarch. Then the council and the patriarch-elect write to the pope. He sends a profession of faith, takes an oath of obedience to Rome, and begs for the pallium. (*see below for what the pallium means*) The pope chooses whether or not to accept him. If the pope does not accept the candidate then the nomination devolves on the pope. But if accepted, the patriarch-elect travels to Rome to receive the pallium from the pope, without which he cannot act as patriarch.
Out of about six Eastern patriarchs, three of them are Cardinals, ie priests of the Diocese of Rome and members of the Roman Curia. The Catholic Encyclopedia states: Ã¢â‚¬Å“In the Catholic Church since Eugene IV (1431-47) cardinals have precedence over patriarchs. Uniat patriarchs are elected by a council of all the bishops of the patriarchate and confirmed by the Holy See. They must send a profession of Faith to the pope and receive the pallium from him.Ã¢â‚¬Â
Popes have decreed that, while Eastern churches can hold local councils, Rome must confirm their decisions. Furthermore Rome has decreed that patriarchs must have permanent representatives in Rome, that patriarchs must make an ad limina visit to Rome (to receive instructions etc) every ten years, that the approval of Rome is needed to found dioceses, and that patriarchs cannot resign their office without the approval of Rome.
In regards to Eastern churches that do not have a patriarch, but rather a metropolitan, the pope must confirm the election of a new metropolitan. The pope appoints regular Eastern bishops just as he does for the Latin church, ie a list of candidates is sent to the pope and the pope selects a bishop for them, but the papal choice does not have to be from the list submitted to him.*** Note: to confer the pallium means to confer jurisdictional rights. Wikipedia and the Catholic Encyclopedia state:
"The Pallium or Pall is an ecclesiastical vestment in the Roman Catholic Church, originally peculiar to the Pope, but for many centuries bestowed by him on metropolitans and primates as a symbol of the jurisdiction delegated to them by the Holy See."
"The evolution of this character was complete about the end of the eleventh century; thenceforth the pallium is always designated in the papal Bulls as the symbol of plenitudo pontificalis officii. Ã¢â‚¬Â¦
"Worn by the pope, the pallium symbolizes the plenitudo pontificalis officii (i.e. the plenitude of pontifical office); worn by archbishops, it typifies their participation in the supreme pastoral power of the pope, who concedes it to them for their proper church provinces. An archbishop, therefore, who has not received the pallium may not exercise any of his functions as metropolitan, nor any metropolitan prerogatives whatever; he is even forbidden to perform any episcopal act until invested with the pallium. Similarly, after his resignation, he may not use the pallium; should he be transferred to another archdiocese. He must again petition the Holy Father for the pallium. Ã¢â‚¬Â¦
"The use of the pallium among metropolitans did not become general until the ninth century, when the obligation was laid upon all metropolitans of forwarding a petition for the pallium accompanied by a solemn profession of faith, all consecrations being forbidden them before the reception of the pallium. The object of this rule was to bring the metropolitans into more intimate connection with the seat of unity and the source of all metropolitan prerogatives, the Holy See, to counteract the aspirations of various autonomy-seeking metropolitans, which were incompatible with the Constitution of the Church, and to counteract the evil influences arising therefromÃ¢â‚¬Â¦
"The oath of allegiance which the recipient of the pallium takes today originated, apparently, in the eleventh century. It is met with during the reign of Paschal II (1099-1118), and replaced the profession of faith. Ã¢â‚¬Â¦
"The symbolic character now attached to the pallium dates back to the time when it was made an obligation for all metropolitans to petition the Holy See for permission to use it. The evolution of this character was complete about the end of the eleventh century; thenceforth the pallium is always designated in the papal Bulls as the symbol of plenitudo pontificalis officii.