"Leland Vandervort" wrote in message
...

Does the concept of "P1S" (Pilot in command under supervision) not
exist in the US? When operating thus, the client would be PIC under
supervision, but the captain would be the instructor/examiner.

Not as described above.

You can be PIC while receiving instruction, but you have to meet the
requirements for PIC. If you don't, then the instructor must be PIC and
meet the requirements for that. An odd quirk is that you can log PIC
while the instructor is PIC, but that's not material here.

In europe, for example, when you take your PPL flight test, it is
taken as P1S. If you pass, it counts as PIC time, and if you do not
pass, it is simply P/UT (Pilot Under Tuition) time.

In the US there is special dispensation given to student pilots to allow
them to be PIC on their flight tests. Actually, there is no strict requirement
that the examinee be PIC on flight tests either.