A church founded in the teeth of the Arian heresy, the Ethiopian Church was under the auspices of the Patriarchate of Alexandria, and at that time Athanasius, the East's champion of orthodoxy against Arianism (Hilary of Poitiers was the champion in the west), was a significant influence over the Ethiopian Church which subsequently venerated his name and resisted every attempt by Arian emperors to bring Ethiopia under its sphere of influence.
Whilst the Church is not inconsiderable in size, its bishop has always been Egyptian, appointed from Alexandria. The Ethiopian Church therefore followed the Egyptian (Coptic) Church when the schism occurred subsequent to the Council of Chalcedon. (Please do not ask me to explain this schism, it's ridiculous.)
In the 7th century Christian Ethiopia was effectively cut off from the rest of Christendom by the rise of Islam, but throughout maintained its Christian character. There was still traffic with the parent patriarchy of Alexandria, of course.
During the Middle Ages communications were opened with Europe, and the Roman Catholic Church sent Jesuit missionaries who reported that the Ethiopians were followers of the same monophysite heresy as the Copts. For whatever reason (and we can well imagine) the Jesuit mission was expelled a couple of decades after its establishment.
In more recent times the Church in Ethiopia campaigned for autonomy, claiming the Coptic hierarchy was too far removed from the lives and daily affairs of the Church. Such processes are inevitably slow and riven with politics, but a settlement of recognition was eventually agreed and in 1926 the Ethiopian Church became an autonomous institution.
