Captain logs PIC or P1 in old speak.
The FO doesn't log PIC they log the PICUS but still have the the Captain down as PIC.
It differs country to country and even between companys. In the UK the FO's tend to log any PF sector as PICUS and the captain doesn't sign their log book. Then they get a letter off the company saying thier hours are correct and the CAA will take that for ATPL issue.
The reason why they have it is so that pilots who go straight onto multicrew can build the required PIC time for ATPL issue.
Personally I have never logged it I had enough PIC time as an instructor and the folk that do tend to have to go back and rejig things when they get upgraded because it screws with your hours when you are applying for jobs because then companys arn't interested in PICUS time.