Jagman - "Something about the PF using the PNF as his 'personal autopilot' is the way it was explained to me." But if the PNF is acting as personal autopilot, would he not be PF? In fact BA use "Handling Pilot" (HP) and "Non-Handling Pilot" (NHP).
To answer the original question, BA do it like this:
P1 (the pilot in charge of the sector) does all the management as well as taxying, doing the take-off, climb, cruise and landing. In between the P2 (the "co"-pilot) will fly the descent and approach. This is called the "monitored approach" and lets the P1 who will land the aeroplane get his eyes out of the windows early to pick up the visual references ASAP which saves that awkward transition from instruments to visual at a late stage.
As P1 runs the show, P2 does engine starts. The NHP reads checklists and does the R/T etc (just like almost everyone else).
During Take-off the HP (even if itīs the FO) gets to handle the thrust levers and make "Stop" calls is the situation merits.
A number of airlines use exactly the same procedures (easyJet for one) apart from the sole difference of not having the "monitored approach".
Thereīs a lot of Bulls**t talked about BA SOPs, mainly by people who don't fly for BA and know the SOP!!! I teach it every day so have a fair idea what it's about!