Okay. There is
no such thing as P2 in aircraft that are certified for single pilot operation (that is, anything that does not expressly require two pilots as a condition of the aircraft's operation. If you can fly it solo, it means it must be a single pilot aircraft).
With that in mind, there are only
three likely operating capacities you can log a flight as (in a single pilot aircraft):
- Pilot in Command (P1) - fairly simple. Means no-one else in the aircraft can log anything of any kind (unless you hold an Instructor rating and you're instructing)...
- Pilot under Training (P U/T) - you're 'dual' and under instruction of someone (who, incidentally, must hold an Instructor rating of some kind -- ANO 2009 53(2)(b) refers...)
- Pilot in Command under Supervision (PICUS or P1/S) - is rare and very specifically for flight exams or tests you pass. Not for a general 'club checkout' or the like.
So, with that in mind, the questions are: a) were you legally allowed to operate as pilot in command (with respect to insurance on the aircraft etc) and b) did you act as pilot in command? If the three month layoff put you outside of, say, club currency or insurance limits and you weren't allowed to be in command without a dual check, then it's fairly obviously P U/T, and the instructor logs P1. If the instructor was pilot in command, then you can
only log P U/T as you can't be P1 (not first pilot), P2 (can't have two pilots in a single pilot aircraft) or P1/S (as you're not completing a test or examination for a rating, or on an integrated course towards an ATPL and acting under the supervision of an instructor)...
For some reason, I can't find the references for this any more, but they should all be lurking in JAR-OPS somewhere (1.080?) -- I don't know if that's been superceded by EASA Part-OPS yet.