Mxsmanic wrote:
On large commercial airliners with required two-person crews, how are
duties usually divided between the captain and the first officer? Are
there specific rules, or are there simply standard conventions, or
does it vary by airline/pilot, or what? Who flies the airplane at
which time,

As directed by the Captain. "Typically" one flies the plane and works
the throttle, the other watches the instruments and calls out the V
speeds for rotate, gear, flaps, etc. and clears the operation of same
with the Captain, if they are not the Captain. The Captain may allow
the FO to act as PIC, but is ultimately responsible for all aspects of
operation.

Part of the job of being a Captain is to groom FOs for Captain, so
there is no "standard" by which all airlines or crews operate, except
according to the manufacturer's POH.

and what does the non-flying pilot do during those times?

Makes airplane noises.
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- gpsman