Interesting. So was the Irish Church independent or was it under an Eastern authority? Either way, it's strange because I always thought that the Pope was the "Bishop of Rome and all the West" or something along those lines.
The Irish Church was independent. The thing to be bear in mind with regards to "all the West" is that the Patriarchates (including the Roman one) were actually a later development. The earliest Church structure above the level of the individual bishop (reflected in both the Apostolic canons and the canons of Nicea) was at the provincial level. The bishops of each Roman province formed a local synod under the chairmanship of the bishop of the provincial capital (the Metropolitan)--in modern terms, each province was an 'autocephalous Church'. Thus when St. Cyprian, as bishop of Carthage and thus Metropolitan of North Africa, got into into a dispute with St. Stephen, bishop of Rome, in the 3rd century, it was a case of a dispute between equals rather a rebellion by a subordinate bishop against his Patriarch (which is why St. Stephen threatened to break communion with the North Africans rather than deposing and replacing their bishops).
Due to their prestige, size, and all-around importance (in both civil and religious terms), Rome, Alexandria and Antioch were always special cases, but early on this prominence consisted more of informal influence than actual authority. At the time of Nicea, Alexandria was 'Metropolitan' to 3 provinces rather than one and Rome was Metropolitan for all the provinces of Southern Italy, but their formal authority (to approve bishops, to call synods, etc) did not extend beyond this. Over the following centuries, a number of different factors resulted in two more cities (Constantinople and Jerusalem) being added to their number and the formal authority of each of these archbishops expanding to incorporate more and more of the previously independent provinces, until by the late Council period we have the Pentarchy where most of Christendom fell under the direct jurisdiction of one of the five great Archbishoprics (by now being called Patriarchates).
A case in point is the province/island/Church of Cyprus which the Patriarchate of Antioch tried to absorb in the 4th century. Fortunately (from the Cypriot's point of view), this attempt coincided with the calling of the 3rd Ecumenical Council, a council at which Antioch was in a relatively weak position. Cyprus was thus able to get an Ecumenical Council to affirm their autocephaly so that even at the height of the Pentarchy, Cyprus remained an independent Church.
Ireland was like Cyprus in being a relic of the earlier period. Ireland received its Christianity primarly from Roman Britain, Gaul, and a Roman missionary or two. But it did so at at a time when the far Western Roman provinces were themselves independent Churches (before they had come under the direct jurisdiction of Rome). Between it's placement on the far edge of the known world and the fact that it was never politically joined to Rome or the Holy Roman Empire, Ireland was basically the last part of the West to be absorbed into the "Patriarchate of the West" as a formal matter (and yes, this does tie to Roman sanction of Norman conquests in Ireland in the 12th century).