Smith regenerates into the new Doctor at the end of the Christmas Special which is traditionally shown either Christmas or Boxing Day. That means we are around 2-3 hours of runtime (allegedly the 50th is now back to being 90 minutes) away from him disappearing from the show.
Less than a full series? The only Doctor who has had that distinction (up to now!) is McGann who had the single US tv movie outing. The next time Doctor Who started up it was Ecclestone, apparently mere hours/days after regenerating from his previous incarnation. He had a single full season and was replaced by Tennant after sticking to his original plan of only doing a single season to help the show get off the ground again.
Less than a full series? The only Doctor who has had that distinction (up to now!) is McGann who had the single US tv movie outing. The next time Doctor Who started up it was Ecclestone, apparently mere hours/days after regenerating from his previous incarnation. He had a single full season and was replaced by Tennant after sticking to his original plan of only doing a single season to help the show get off the ground again.