You are illustrating that you are not educated, at least on this topic.  Consider that during these times the Church was suffering through the persecutions of Decius and Valerian.
Stephen did not "wrestle" control.  He was the legitimate bishop of Rome.  The only one (at that time) who tried to usurp the papacy was Novatian, the first anti-pope, shortly after Cornelius had legitimately ascended the papacy.  Novatian had the support of just 3 bishops; certainly too underwhelming a number for any sort of credibility.  All of the African bishops, including Cyprian, supported Cornelius.  Stephen succeeded Cornelius. Cyprian certainly recognized and accepted his authority as such, writing him early on urging him to appoint a new bishop at Arles, where the current bishop had become a Novatianist.  What prompted Cyprian to write his treatise, "On the Unity of Christian Faith", was the Novatian Schism...