What would happen if the German battleship Tirpitz doesn't accompany her sister ship Bismarck on Operation Rheinübung?
IOTL, Admiral Lütjens was hesitant to take a brand-new ship with a green crew with him on the sortie, but Großadmiral Raeder insisted on having an additional capital ship for insurance, and the Scharnhorst twins were unavailable.
I think had the Bismarck not been slowed down by Tirpitz then she might have been able to break out into the Atlantic and not have been engaged by the Home Fleet at all
As it was the number of systems issues that Tirpitz suffered before a single shot was fired eventually dooming all 3 ships.
Had Tirpitz not accompanied Bismarck and Prinz Eugen then the 'fleet' might not have been slowed down so much
I guess its easy to criticise Lütjens for not splitting up the 3 ships as soon as they were discovered in a vain attempt to save the Tirpitz - but the Tirpitz was their sister ship and its unlikely that they would not turn and come back for her.
The results of the subsequent battle are well known - despite heavy damage to some of the British ships - all 3 German Ships were badly damaged and this allowed subsequent British heavy Home fleet units as well as 2 TB Strikes from HMS Victorious to finish them off.
As Vice Admiral Holland said to his Captains after the battle "I hope that if any of you are ever called upon to lead a ship into action against an opponent many times superior, you will command your ship as gallantly as Bismarck was commanded today"
Now had Bismarck sortied on her own (with or without Prinz Eugen) then its possible that she might have achieved some sort of operational surprise and managed to break into the North Atlantic.
Whether she would have achieved anything of worth is open to debate and given the discrepancy of forces it is likely that she would have been hunted down or forced to run to France
I think in light of what happened it was a classic example of Germany putting all of their eggs into one basket
They would probably have served their cause better by keeping the ships as a 'fleet in being' i.e. threatening to sortie - this would have prevented the British from subsequently sending so many ships to the Med and later the far east - tying down many heavy units as part of the Home Fleet.
For example the British had lost several Cruisers covering the evacuation of Crete at this time - but with the loss of both German Battleships the RN were able to make good those losses in a matter of weeks from those forces no longer required in Britain.
I suspect that had one or both of these battleships have survived then the 4th and 5th KGV Battleships might have been given priority over the 2 Implacable Fleet carriers and done more than escort BPF carriers at the end of the war and Who knows maybe HMS Vanguard might have been completed.