No one has to initiate any process of handing over the reins.  It's not up to a sitting president, or any other person.  No court case is needed.  It's stated clearly in the 20th Amendment:
	
	
		
			
				
			
			
				
				
				
					
						
							
						
					
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If anything, after noon on Jan 20th Trump could be evicted from the White House as an intruder.  I personally would like to see him hand-cuffed and perp-walked out the door, past reporters and cameramen, to black Secret Service SUVs waiting on Pennsylvania Ave.  But sadly, those details aren't spelled out in the 20th Amendment.