In Easa's Part-FCL search for PICUS (you'll get the exact same results in AMC+GM)."Pilot-in-command under supervision" (PICUS) means a co-pilot performing, under the supervision of the pilot-in-command, the duties and functions of a pilot-in-command.
FCL.035 Crediting of flight time and theoretical knowledge: Flight time as co-pilot or PICUS. Unless otherwise determined in this Part, the holder of a pilot licence, when acting as co-pilot or PICUS, is entitled to be credited with all of the co-pilot time towards the total flight time required for a higher grade of pilot licence. Logging of time - PIC flight time: a co-pilot acting as PICUS on an aircraft on which more than one pilot is required under the type certification of the aircraft or as required by operational requirements provided that such PICUS time is countersigned by the PIC; PICUS flight time:provided that the method of supervision is acceptableto the competent authority, a co-pilot may log as PIC flight time flown as PICUS when all the duties and functions of PIC on that flight were carried out in such a way that the intervention of the PIC in the interest of safety was not required. Format of the record:When an aircraft carries two or more pilots as members of the operating crew, one of them shall, before the flight commences, be designated by the operator as the aircraft PIC, according to operational requirements, who may delegate the conduct of the flight to another suitably qualified pilot. All flying carried out as PIC is entered in the logbook as ‘PIC’. A pilot flying as ‘PICUS’ or ‘SPIC’ enters flying time as ‘PIC’ but all such entries are to be certified by the PIC or FI in the ‘Remarks’ column of the logbook. Notes on recording of flight time: column 10: pilot function time: (i) enter flight time as PIC, SPIC and PICUS as PIC; (ii) all time recorded as SPIC or PICUS is countersigned by the aircraft PIC/FI in the ‘remarks’ (column 12); column 12: the ‘remarks’ column may be used to record details of the flight at the holder’s discretion. The following entries, however, should always be made: signature of PIC if the pilot is recording flight time as SPIC or PICUS;
Basically:
SINGLE PILOT:
- for someone to be under instruction (and to put in hours as instructor onthe other side), you have to be under training regime (training records, programme, etc.)
- when you have an official check, you are basically fyling as PIC, but the official PIC is the examiner - hence, you are the PICUS (you are acting as PIC)
MULTI PILOT:
- instruction - look the paragraph above
- dual: one is PIC other SIC, the SIC is not performing as PIC
- PICUS: the SIC is acting as PIC, and the PIC is not "interfering" with PIC-ing of the SIC.
BONUS:
- SPIC: when you are under instruction, but the instructor lets you to act as PIC.