I'm wondering some more about how jurisdiction is understood in the OO tradition. It seems that a number of the concerns expressed in the Byzantine tradition are not in the OO tradition.
For one thing, explicit formulation and establishment of the Pentarchy came significantly after the split.
For another, there is the common "barbarian lands" issue where Constantinople is often regarded as having authority in the "barbarian lands" because of Canon 28 of the Council of Chalcedon. But Chalcedon wasn't accepted by the Orientals, so it would seem its canonical establishments would have no bearing.
Finally, there is the fact that before Chalcedon it was understood that the area of each Roman civil diocese had its own primate (Alexandria in Egypt, Antioch in The East, Ephesus in Asia, etc.), but Chalcedon gave Constantinople jurisdiction over not only its own diocese (Thrace) but also that of Asia and Pontus, overthrowing the total primacy of Ephesus and Caesarea in those areas. It would seem this establishment would also have no bearing in the Oriental tradition. But even more concretely in this situation, the Third Council of Ephesus repudiated this canon and returned the primacy of Asia back over to Ephesus.
It would seem that because of these points that the Orientals would have developed a slightly different understanding of jurisdiction from the Byzantines. Can someone explain the substance behind this?