No. We do not have the equivalent of a Roman pope either, at least in its post-Gregorian Reformation context.
Instead, we have bishops, archbishops, metropolitans, and patriarchs. An archbishop, metropolitan, or patriarch may be the head of an autocephalous church. There are about a dozen of those, each governing itself and being in communion with the others--for example, the Patriarchates of Alexandria, Jerusalem, Antioch, Constantinople, Moscow, Serbia, Romania, Bulgaria, etc. There is no superbishop like the Roman pope of the last 1,000 years who exercises jurisdiction over the whole world.