Dear brother deusveritasest,
For instance, a bishop of the Syriac Patriarchate cannot appeal to HH Pope Shenoute.
I don't think that's entirely true. I am sure that if a Syriac Orthodox Metropolitan was having trouble with the Patriarch and believed him to have fallen into heresy, that he would be within his rights and duties to appeal to the Coptic Pope, who has a history of presidency at pan-jurisdictional gatherings and is logically now primus inter pares of the Oriental communion, for the convoking of a Pan-Oriental Conference to address the matter.
But you are right in so far as there is no prerogative of appeal to Alexandria in and of itself.
The Supreme authority of an autocephalous Church is the Synod. If a Syriac Metropolitan has a problem with the Patriarch, there is no greater authority to which he can appeal except the Synod.
It is different between the Coptic-Ethiopian-Eritrean Churches. The Ethiopian and Eritrean Churches are autocephalous by canon and in principle, but they are functionally autonomous with respect to the See of Alexandria.
But the Catholic Church affirms the ancient canons in this respect.
You say that as if we are overlooking and ignoring the canons of Sardica. Even if they are upheld as authoritative (I don't know as its merely a local council with regards to the Oriental ecclesiology), the canon is no longer applicable on the premise that there is no longer a bishop of Rome within the Church.
A bishop in any Patriarchate can appeal to the bishop of Rome. In that sense, Patriarchates within the Catholic communion are not strictly autocephalous.
I get your point here. Because Rome has the prerogative of intervention with these churches, they are not strictly autonomous or autocephalous. I had already imagined that to be the case. But I want to know in the context of their typical everyday administration, as I assume real intervention from Rome is not all that common.
Rome does not at all intervene in the day-to-day affairs of the non-Latin Patriarchal Churches. The Vatican Council did not grant him the prerogative to do that (contrary to the claims of many – both Catholics and non-Catholics).
But the Pope does have the authority to enforce a universal canon of the Church on local Churches. For example, the requirement to elect a Patriarch to a vacant see within a prescribed time period is a universal canon of the Church. If a local Church is found violating it, the Pope does have the authority to step in. This occurred a few years ago in the Chaldean Catholic Church (IIRC). The Patriarchal See had been vacant for over a month, though universal law states (IIRC) it must be filled within 20 days (indeed, no Church should be without its chief pastor). I believe the Pope waited another 2 weeks past the deadline before he intervened.
But day-to-day administration? No. In Catholic canon law the day-to-day administration of a Church belongs to the proper
ordinary. The word “proper” is a distinctly canonical term referring to the local ordinary who has the inherent authority to administer the day-to-day affairs of his Church. Whatever other descriptives one may attach to the office of the Pope (immediate, ordinary, supreme, etc.) with respect to a local Church, the canonical term “proper” is not one of them.