Machinbird;
"Who was flying?" would have to be one of the key questions that the accident investigation would have to settle.
Here, I
will speculate based upon experience in long-haul flights on the Atlantic and Pacific including the ITCZ.
Machinbird, CONF iture, Chris, I know you and perhaps others reading this, will be familiar with the following but some may not be.
In my experience it was more often the case that the captain flew the first leg and the first officer flew the next leg, etc.
If rostering, (especially for short-haul domestic), was such that a captain and first officer were assigned flights together for the month, the captain could change the pattern so that the first officer started the day and the captain took the next leg. (Perhaps some here can recall 80+ entries into the same darn airport in the same month...)
With the introduction of a relief pilot (for those not familiar...the RP is checked on the airplane, but not licensed for flight below cruise altitude), for long-haul work, the rostering process changed slightly. There are different ways to roster crews, and they have been discussed here before.
In the way to which I was accustomed, the captain, in consultation with the crew, assigned the crew rest rostering for the flight. There were no formal rules regarding rests, who was first, second, etc - it was left up to the crew. In our arrangement, the captain had first choice and it would go from there. If someone was really needing a break, (lousy sleep, noisy room, a dozen other reasons, etc) then that crew member could be offered first choice.
A second way, with which I am not familiar, would be laid out in airline policy and/or SOPs which the crew must follow, (with possibilities for variations of circumstance). Others can detail such procedures but I have the impression that it is more formally addressed at AF and the breaks will be taken as assigned.
There are benefits and problems with either procedure. I'm not going to detail them here.
Without intending anything other than conveying how we conducted rostering, I was up front during any ITCZ transition unless I knew the weather over the 3hr-or-so transit was benign.
If I flew the first leg, the next leg would be the first officer's. When on break, the relief pilot would occupy the left seat and the first offficer would fly from the right seat. When the first officer was on break, the RP would occupy the right seat and continue the duties of the first officer, whether flying or communications.
The RP was legally required to be on the flight deck from taxi to top-of-climb, at which time s/he would change with the first to go back for a break. For us, the rostering was discussed during the climb and times assigned for return-from-break, with a way to signal the pilot who would either be in the bunk just behind the cockpit or in a Business-class seat in a "tent" arrangement, that it was time to return to the cockpit. It was usually a 10-minute or so call to provide time to change and to wake up and possibly arrange a meal to be brought up when settled in the seat again. We often hung around the galley for these few minutes both going to and coming from break, just chatting with the galley folks and a passenger or two.
The A340 bunk was noisy and cramped. Compared to the B777, it was unacceptable. The A330 I'm familiar with had a "tent" arrangement and other than the mild discomfort of preparing for rest and arising after in reduced privacy, it was sufficient as the seat would go just about flat.
Determining breaks was straightforward. A half-hour would be added to the wheels-up time for top-of-ciimb time and the same amount subtracted from arrival time. The remaining time (essentially the cruise flight time) would be divided, almost always equally, between the three, or sometimes four crew members. If four, two would go back together.
On a ten hour flight, there would be about nine hours to divide between the pilots.
This is because first break would begin at top-of-climb, about a half-hour out and, in the case above, (3hrs each) would give about two-and-a-half hours of rest plus a bit of time in the galley area behind the cockpit, as described above. It isn't a good idea to get into deep (REM) sleep but it was also hard to avoid - one certainly wanted to avoid deep sleep, waking up just before top-of-descent.
Before crew-change point, a formal briefing would be conducted by the crew, for the crew member returning from break. Position, altitudes, pending clearances, any weather, fuel state, aircraft performance, communications...(which ATC was next to be called), etc and the seat change would occur. The last crew member on break would normally be brought up a bit earlier to ensure wakefulness for the descent, approach and landing.
With locked-cockpit doors, entry was formal and accomplished through secure procedures.
In the case of AF447, I think the captain probably flew down to Rio. In fact, who flew down might already be known through informal discussion with others who may have interacted with the crew on the layover or in dispatch the next day.
If the captain flew the leg down, that means that the first officer would likely be flying the trip home.
I have always interpreted the finding of the captain's body, as evidence, (not incontrovertible of course) that he was either in the galley area or in a business class (double) seat. I am unsure if AF's A330's have a bunk. If not, the business-class crew rest seat is the other cockpit crew-rest location; someone mentioned that cockpit crew do not use the F/A crew rest facility and they are correct. It is downstairs, mid-section of the aircraft and an unacceptable distance from the cockpit should a crew member's presence be urgently required.
If the captain was in the cabin then the RP would be in the left seat. He would be doing the communications work and flight plan log-keeping.
The pilot flying engages the autopilot associated with his seat position...left seat or right. If the first officer flies, the #2 autopilot is engaged. The #2 MCDU is the "master" and the #1 the slave, each associated with its respective FMGEC which becomes "master" or "slave"; #3 MCDU is used for ACARS, ATSU, AOC and ACMS communications and aircraft "health" functions.
The flying pilot can be thus determined by which autopilot was engaged - it would be rare for the "offside" autopilot to be used, especially here as there were no snags preventing use of both APs.
This is a bit long, but the actual crew-rest/break process hasn't really been discussed I believe, and perhaps it would help understand some things.