Is the Catholic church a continuation of the Roman Empire?

When you read about the Roman Empire in history in particular the practices of it's government it seems like it to me. The Emperor held the title Pontifex Maximus (chief priest of Roman state), and was made a god by the senate after death. Pontifex Maximus is the title of the pope these days isn't it? And people considered particularly holy are made saints these days and prayed to in some cases. I'm not trying to attack Catholicism, just trying to get an idea of where these things come from. The Biblical Saints are all the believers (or saved), and Christ is the head of the Church. And Jesus, when he taught how to pray, only mentions God and not a physical person including himself. Like I said just wondering where these practices come from since not from Jesus (who is the head of the Church).