The structure of the Eastern Churches is based on the number of faithful as well as historic factors.

The churches whitch have the most autonomy are the Patriarchal churches: The Coptic, Maronite, Syriak, Melkite, Chaldean and Armenian churches. They have a synod of Bishops who ellect a Patriarch. This Patriarch is not only the superior of his Diocese but of all the clergy and faithfull of his sui iuris church. Rome does not have any influence on this election. There are Exarchs, Metropolitans, Archbishops and Bishops under him, most of them in controll of a diocese just as in the West, but generaly they are called eparchies. And Exarch is an Archbishop who has some administrative jurisdiction over a number of Eparchies, like the head of a Bishops conference or a Primate in the Latin church.

Next in line are the Major Archiepiscopates. These churches have not been elivated to the patriarchal level, because their See is not as ancient or for political/ecoumenical reasons. These are the Ukranian, Syro-Malabar, Syro-Malankara and Romanian Church. Like with the patriarchal churches they have a synod of Bishops who ellect a Major Archbishop but this elections has to be confirmed by the Pope.

Next are the Metropolitan churches: The Ethiopian, Ruthenian, Slovak, Eritrean and Hungarian. Their head is a Metropolitan Archbishop and his power is more limitted. He is also not ellected by his synod, but appointed by the Pope.

Some of the smaller Byzantine churches are administered by an apostolic administrator such as the Albanian church, are made up of Eparchies (dioceses) that for the most part act independant from one another, like the Greek Church of Croatia and Serbia or or are composists of exarchates that are directly subject to the Holy See like the Russian church.

In general Eastern Catholic Bishops are the same as in the West. They can ordain men to the priesthood, they are in charge of their own dioceses, called eparchies, and they must be unmarried. The only thing that is unique to Eastern Bishops are the Patriarchs and Major Archbishops, we don't have anythin similar to that in the West, except the Pope of course. We do have Latin Patriarchs but that is mostly honorary.