So the FO when PF vacates the runway. I believed captain to take control while decelerating on the runway
This was the case on the 737's because they only had a tiller on the Captains side.
On the Airbus, when Pilot Flying the FO will control start up, push back, taxy out and every phase of the flight right up to the point when the aircraft is just about to park on stand. FO's don't park the aircraft because a lot of stand guidance systems are designed for left hand seat only.
Hope this helps.