"He said therefore to them again: Peace be to you. As the Father hath sent me, I also send you. 22 When he had said this, he breathed on them; and he said to them: Receive ye the Holy Ghost. 23 Whose sins you shall forgive, they are forgiven them: and whose sins you shall retain, they are retained."
On what basis do you believe that the supernatural powers given to the Apostles were passed on?
Via the laying on of hands, specifically with Paul. If God was to imbue men with the full power of the Holy Spirit through nothing more than His Will, then certainly Paul would be morth worthy of such an honor than anyone else throughout history. The fact that, after God had chosen Paul, the Apostles laid hands upon him to confer their gift goes a long way is supporting the passing on of the gift.