Let’s talk patriarch, says Vatican II. “Eastern Rite Patriarchs” are the topic of the next chapter which begins with section 7:
The patriarchate, as an institution, has existed in the Church from the earliest times and was recognized by the first ecumenical councils.(Cfr. Synodum Nicaenam I, can. 6; Constantinopolitanam I, can. 2 et 3; Chalcedonensem, can. 28; can. 9; Constantinopolitanam IV can. 17; can. 21; Lateranensem IV can. 5; can. 30; Florentinam, Decr. pro. Graecis; etc.)
By the name Eastern patriarch, is meant the bishop to whom belongs jurisdiction over all bishops, not excepting metropolitans clergy and people of his own territory or rite, in accordance with canon law and without prejudice to the primacy of the Roman Pontiff.(Gfr. Synodum Nicaenam I, can. 6, Constantinopolitanam I, can. 3; Constantinopolitanam IV, can. 17, Pius XII, Motu proprio Cleri sanctitati, can. 216; 2, 1 .)
Wherever an hierarch of any rite is appointed outside the territorial bounds of the patriarchate, he remains attached to the hierarchy of the patriarchate of that rite, in accordance with canon law.
Some of us often grouse about the lack of patriarchal action in the West, namely that Africa, the Americas, or southern and eastern Asia don’t continue the traditional practice of establishing patriarchs.