I don't know if historians consider this to be true today but the catholic church recognized Charlemagne and later the HRE (Holy Roman Empire) as the successor state/next Rome.
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As far as the Ottoman Empire was concerned they proclained they were the successor state to the Romans. They controlled the last vestige of Roman power while also owning most of the territory the Roman empire had once owned.
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Then you have Czarist Russia. Being as the Byzantines who controlled Constantinople (at the time named Byzantium) were Eastern Orthodox christian. The Czar claimed that with the fall to Muslim invasion that Russia being the largest Eastern Orthodox empire was therefore the 3rd Rome.
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As far as the Ottoman Empire was concerned they proclained they were the successor state to the Romans. They controlled the last vestige of Roman power while also owning most of the territory the Roman empire had once owned.
-
Then you have Czarist Russia. Being as the Byzantines who controlled Constantinople (at the time named Byzantium) were Eastern Orthodox christian. The Czar claimed that with the fall to Muslim invasion that Russia being the largest Eastern Orthodox empire was therefore the 3rd Rome.