Can. 43 The bishop of the Church of Rome, in whom resides the office given in special way by the Lord to Peter, first of the Apostles and to be transmitted to his successors, is head of the college of bishops, the Vicar of Christ and Pastor of the entire Church on earth; therefore, in virtue of his office he enjoys supreme, full, immediate and universal ordinary power in the Church which he can always freely exercise.
Can. 55 According to the most ancient tradition of the Church, already recognized by the first ecumenical councils, the patriarchal institution has existed in the Church; for this reason a special honor is to be accorded to the patriarchs of the Eastern Churches, each of whom presides over his patriarchal Church as father and head.
Can. 56 A patriarch is a bishop who enjoys power over all bishops including metropolitans and other Christian faithful of the Church over which he presides according to the norm of law approved by the supreme authority of the Church.
Can. 58 Patriarchs of Eastern Churches precede all bishops of any degree everywhere in the world, with due regard for special norms of precedence established by the Roman Pontiff.
Rome wrote the Code of Canon Law, and many Eastern Catholic hierarchs aren't the bit pleased with it.
First of all, no pre-1054 Eastern Christian recognized that the pope had the right to intervene in the internal affairs of the Eastern churches unilaterally. Pope Nicholas' uncanonical, unilateral, intervention in the case of St. Photios is a prime example because there was no appeal, and Fr. Dvornik has proven this was the case.
The patriarchs and their Holy Synods should have the right to elect and appoint their own bishops without papal approval based upon custom. No pre-schism pope appointed any Eastern patriarchs or bishops.
The papal claims to direct jurisdiction in the East were never recognized in the East.