RedactedNarrative: Subject was operating his vessel, a 21' remote steer bay boat, in the Gulf of Mexico, on plane.  Operator stated that his vessel began to slow down, so he increased throttle.  As he increased throttle, his vessel did not increase speed.  Operator stated that he turned around and he had water in the stern area of the vessel.  Operator looked at the motor, and it appeared to be hanging at an odd angle, lower than normal.  The operator then throttled down to an idle, and the motor fell off the back of the vessel and was hanging by the steering hoses and wires.  Vessel began flooding. USCG was able to locate the subjects and tow them to the Cameron Jetty boat launch.  Vessel was equipped with adequate PFD, but they were  not used.  Vessel was equipped with an ignition safety switch, but it was not used.  Outboard motor was cut from the vessel by the USCG for towing.  Motor was not recovered.