Did the papacy develop over time, as it is today?
The Church is a living organism. And as such, She has changed over the years. This change is much like the changes that a young child may go through as it grows up. Although he may look different, he’s still the same person. In this way, the need for the Papacy has changed over the years, and thus I feel the Papcy has grown and even receded as the needs of the Church have dictated.
When you look at the first 300 or so years, when the first 31 popes were executed by the Roman authorities, the Papacy had nowhere to go but up, as you could well imagine.
The Bishop of Rome always had the same authority, but it is not always exercised in the same way.