Q:

What's the command that Kirk gives when he turns over command?

Which is correct, A or B? As he turns over the command, Kirk says

A) 'You have the COM' [as in Command]  

or  

B) You have the CONN.' [as in ???]

I've always assumed the former, A, is correct, but a recent television commercial for the new Star Trek app, claims B, which has left me thoroughly confused. 

A:

The command is "you have the conn", as can be seen in this original screenplay from Star Trek: The Motion Picture

KIRK: Mr. Decker, I'd like to see you in my quarters.
(toward helm)
You have the conn, Mr. Sulu.

The term "conn" is a naval/nautical expression;

One of the most important principles of ship handling is that there be
no ambiguity as to who is controlling the movements of the ship. One
person gives orders to the ship's engine, rudder, lines, and ground
tackle. This person is said to have the "conn."
— James Alden Barber, 2005, "Introduction", The Naval Shiphandler's Guide, p. 8.

The etymology is lost, but it may have something to do with the conduct of the vessel.

