I did five legs in a row without an FO. 3/5 we had three captains. The other two legs, we had four captains.
Where I fly, the senior capt, in consultation with everyone, decides who will sign for the aircraft and who will be in which seats for landing/takeoff, and who will fly. On my flights, the Capt signing for the aircraft has always sat in the left seat for TO/Landing.
All FOs r pic qualified, and all capts r right seat qualed.