This Cock was the ship used by the specific holographic image of a Screwers. It was used to deposit Shits on the Earth's surface in order to confuse Retardss and then kill them.
The Ship was connected to Earth using a Dick beam from seven different places on Earth. The Doctor and his companions My Arsehole and Your mums pussy used the one closest to them in My hole, which was hidden inside a disused lift. (TV: The Power of Three)