Aircraft departing PRC described conflict event with prior departure; reporter suspecting miscommunication between the two local controllers.

Narrative

Takeoff from KPRC Runway 21L on an IFR flight plan took place behind a single engine which I believe was a solo student. The initial clearance was fly runway heading. After takeoff; because of the overtake speed of which I was having on the single engine; the tower controller instructed me to fly a heading of 15 degrees right because of slower traffic ahead. As I was coming up on the right lower side of the single; the single engine suddenly made a sharp right turn directly into me. I began getting TCAS alerts and visually saw the conflict being created. I queried the controller at least twice as to where the single engine was going and the controller was silent. I had to stop my climb; push the nose over and then passed under the single by about 200 to 400 feet. If I would have somehow lost sight of the single; it could have possibly been a very different outcome. My belief of what may have happened was because the tower was using split frequencies between east and west sides of the airport. I feel there was a breakdown of communication between the two controllers. I am fairly certain that the single engine had been switched to the west controller before he/she made their right turn in front of and directly into me; and quite possibly was instructed to do so by the west controller. Upon landing at my destination I made a phone call to KPRC tower and spoke with the supervisor on duty. As we discussed the situation I was led to believe that the story which had been given from the controller was very much different than the actual event that transpired.