Did Hippolytus Succeed Gaius to the Office 'Bishop of the Nations'?

On the whole the evidence seems to preponderate in favour of the view taken by Dr. Dbllinger that Hippolytus was the first of the Antipopes, and if only the Greek part of the Romish Church owned his jurisdiction, this may account for his being called 'the bishop of the nations.' (See Philosoph. x. 31, 32, 34, where he alludes to Gentiles as being under his special care) [Frederic William Farrar, Lives of the Fathers p. 89]