As stated above, but to summarize:
Captain: always the aircraft commander (unless two Captains, special case*) therefore always: P.1
F/O: if handling pilot: PICUS or P.1u/s in olde English. (Should be countersigned but nobody bothers.)
.......if non-handling: P.2
A Cruise Captain is not the aircraft Commander and should not be logging P.1
*Some VIP companies crew with two Captains, in this case, before flight, one will be designated commander, and log P.1, the other will log as per F/O above, either PICUS or P.2 dependent on whether handling or not.