Who are the Metropolitan Archbishops and what authority does that have over ordinary bishops?
And what is canon law talking about the authority of Metropolitan Archbishops?
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Authority of Metropolitan Archbishops?
I do not think Wikipedia is a great source to back up an answer. But in this case Wikipedia does an good job in explaining what a metropolitan archbishop is and does. I will add what Canon Law has to say at the end.
In the Latin Church, an ecclesiastical province, composed of several neighbouring dioceses, is headed by a metropolitan, the archbishop of the diocese designated by the Pope.The other bishops are known as suffragan bishops.
The metropolitan's powers over dioceses other than his own are normally limited to:
supervising observance of faith and ecclesiastical discipline and notifying the Pope of any abuses;
carrying out, for reasons approved beforehand by the Holy See, a canonical inspection that the suffragan bishop has neglected to perform;
appointing a diocesan administrator if the college of consultors fails to elect an at least 35-year-old priest within eight days after the vacancy of the see becomes known; and
serving as the default ecclesiastical court for appeals from decisions of the tribunals of the suffragan bishops.
The metropolitan also has the liturgical privilege of celebrating sacred functions throughout the province, as if he were a bishop in his own diocese, provided only that, if he celebrates in a cathedral church, the diocesan bishop has been informed beforehand.
The metropolitan is obliged to request the pallium, a symbol of the power that, in communion with the Church of Rome, he possesses over his ecclesiastical province. This holds even if he had the pallium in another metropolitan see.
It is the responsibility of the metropolitan, with the consent of the majority of the suffragan bishops, to call a provincial council, decide where to convene it, and determine the agenda. It is his prerogative to preside over the provincial council. No provincial council can be called if the metropolitan see is vacant.
The Metropolitans of a given territory are also involved in the selection of bishops. Every three years, they compile a list of provimvedis - a list of priests who may be suitable for the office of bishop. This is forwarded to the local Apostolic Nuncio, who evaluates the candidates in a consultative and confidential process. The Nuncio in turn forwards the best candidates to the Congregation for Bishops in Rome, who conduct a final evaluation of candidates and offer their findings to the Pope for his final decision of appointment. - Metropolitan bishop
As far as Canon Law is concerned here follows the norms put forth by the Church:
Can. 435 A metropolitan, who is the archbishop of his diocese, presides over an ecclesiastical province. The office of metropolitan is joined with an episcopal see determined or approved by the Roman Pontiff.
Can. 436 §1. In the suffragan dioceses, a metropolitan is competent:
1/ to exercise vigilance so that the faith and ecclesiastical discipline are observed carefully and to inform the Roman Pontiff of abuses, if there are any;
2/ to conduct a canonical visitation for a cause previously approved by the Apostolic See if a suffragan has neglected it;
3/ to designate a diocesan administrator according to the norm of cann. 421, §2, and 425, §3.
§2. Where circumstances demand it, the Apostolic See can endow a metropolitan with special functions and power to be determined in particular law.
§3. The metropolitan has no other power of governance in the suffragan dioceses. He can perform sacred functions, however, as if he were a bishop in his own diocese in all churches, but he is first to inform the diocesan bishop if the church is the cathedral.
Can. 437 §1. Within three months from the reception of episcopal consecration or if he has already been consecrated, from the canonical provision, a metropolitan is obliged to request the pallium from the Roman Pontiff either personally or through a proxy. The pallium signifies the power which the metropolitan, in communion with the Roman Church, has by law in his own province.
§2. A metropolitan can use the pallium according to the norm of liturgical laws within any church of the ecclesiastical province over which he presides, but not outside it, even if the diocesan bishop gives his assent.
§3. A metropolitan needs a new pallium if he is transferred to another metropolitan see.
Can. 438 The titles of patriarch and primate entail no power of governance in the Latin Church apart from a prerogative of honor unless in some matters the contrary is clear from apostolic privilege or approved custom.
One could note that every five years a diocesan bishop, this includes metropolitan archbishops, is bound to make a report to the Supreme Pontiff on the state of the diocese entrusted to him, according to the form and time determined by the Apostolic See. These visits ad limina apostolorum* are usually carried out in groups of ecclesiastical provinces that is to say with the metropolitan archbishop and the other bishops of the region.