Goering had sent Hitler a message stating that unless Hitler responded that he would assume that Hitler was incapacitated and would thus assume the leadership of Germany. Hitler was convinced that this was an attempted coup and stripped Goering of his rank and commands and had him placed under arrest.
Himmler had attempted to negotiate with the Allies without Hitler's permission. Orders for his arrest had been put out but Himmler escaped.
Hitler thought that basically everyone was to blame for the loss of the war, were incompetent, etc. Any army leaders he may have wanted to replace him weren't in a position to do so.
Both Doenitz and Goebbels were chosen to be Hitler's successors (Hitler was the only Fuehrer of Nazi Germany), Doenitz as President and Goebbels as Chancellor (these were the positions which had originally being illegally joined into the position of Fuehrer und Reichskanzler by Hitler). Doenitz was chosen because he was basically the only high ranking officer left who Hitler felt hadn't betrayed the Reich. Goebbels was chosen because he was seen as still being loyal since he was in the bunker with Hitler.
Hitler and The End by Ian Kershaw.