Oriental Orthodoxy is a family in communion, not a single church, and it has never had a central authority of any kind.
Six bodies are usually counted. The Coptic Orthodox Church of Egypt under the Pope of Alexandria; the Armenian Apostolic Church, whose structure includes two catholicosates, at Etchmiadzin in Armenia and at Antelias in Lebanon, and two patriarchates, at Jerusalem and Constantinople; the Syriac Orthodox Church under the Patriarch of Antioch; the Ethiopian Orthodox Tewahedo Church; the Eritrean Orthodox Tewahedo Church, which separated from the Ethiopian church in the 1990s following Eritrean independence; and the Malankara Orthodox Syrian Church in Kerala. Each governs itself through its own synod. They recognise one another's sacraments and orders and meet in conference, and that is the whole of the connection.
Liturgically they are the most distinct churches in Christendom. Each keeps its own ancient rite in its own liturgical language, Coptic and Arabic, Classical Armenian, Syriac, Geez, Malayalam and Syriac, and each keeps its own calendar. The Ethiopian and Eritrean churches are the most unusual: they observe a Saturday as well as a Sunday Sabbath in places, practise male circumcision as a cultural and religious norm, maintain the Ark of the Covenant tradition at Aksum, and keep a broader scriptural canon than any other Christian body, including Enoch and Jubilees.
Fasting is the discipline outsiders notice first. The Coptic and Ethiopian calendars together set well over a hundred days a year on which no animal product is eaten, which is a good deal more than most Christians now attempt.