Originally Posted by JohnBurke

Your temporary pilot certificate came with a limitation stating that you must be under supervision for 20 hours, or your employer provided this limitation?

There is only one PIC on board. You are either the pilot in command, or you are not. The King Air 300 requires one pilot under its type certification.

If you log PIC, there's no "sole manipulator PIC. Just PIC. There are several means by which you can log PIC, and sole manipulator of the controls of an aircraft for which you are rated, is one such qualification. You can also log PIC if you are pilot in command of an aircraft requiring more than one crew member under type certification, or the regulations under which the flight is operated (eg, Part 135, etc). It's a single pilot airplane, so the type certification doesn't require a second crew member. If your employer requires one, such as a corporate department that wants a second pilot, that doesn't qualify for a required. second crew member, for the purposes of logging PIC. Regardless, it's simply logged as "PIC."

If there is "another PIC" on board, which if you is actually in command. Who has ultimate authority and ultimate responsibility for the aircraft and the flight? If you're the pilot in command, then log PIC. If the other pilot is PIC, then you're not. If a SIC isn't required, you're also not SIC.

You haven't provided enough information about your operation, the type of regulation under which the flight or aircraft is operated, nature of your employement, etc.