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Typically, the "conn" of a starship, be it a Battlestar or otherwise, is the collective name for the helm controls- yaw, pitch, and roll.
The conn may also be the actual control or command of the ship, and is used metaphorically- that is, the conn in this instance is no one station or console, but is the actual command at a given time and may be held by any officer designated by the Commanding Officer or Officer of the Deck:
"You have the conn."