From
Wikipedia, "Cyril appealed to Pope Celestine I to make a decision, and Celestine delegated to Cyril the job of excommunicating Nestorius if he did not change his teachings within 10 days."
Nestorius' condemnation was not a foregone conclusion when the Council of Ephesus began. Nestorius was the one who helped to get the Council called through his friendship with the Emperor, who supported Nestorius. Cyril was fighting for a reason, and the battle was won at the Council of Ephesus. This claim from
@abacabb3 that Nestorius was always a heretic and the Council played no real role in that reality is untrue to history.