sat 6:15 p.m. the Bismarck confronts its pursuers, the battleship Prince of Wales and the cruisers Norfolk and Suffolk and shots are exchanged -- although no hits. This skirmish provides cover for the Prinz Eugen which speeds up and pulls out of radar range and escapes.
The Prinz Eugen later meets up with a tanker and refuels, but is unable to locate any convoys because the British have diverted them away from the PE's likely hunting grounds. On the 29th the cruiser developed a problem with its engines and headed for France uneventfully. On June 1 the cruiser reached Brest.
One decision I haven't seen examined much was this detachment of the Prinz Eugen. The ship didn't accomplish much and wasn't well suited for the raider role anyway. I wonder if it wouldn't have been better to have the PE continue to accompany the Bismarck. A the very least it added some AA capability. Also worth considering is the possible benefit of having another ship present to confuse attacking aircraft. As it we will see, the aircraft attacking the Bismarck were prone to mistaken identity attacks anyway -- in one case lining up to hit a small American coast guard cutter and in the second case actually attacking a British light cruiser. How much more likely would be a mistaken attack if there were two ships in the same vicinity as similar-appearing as the Prinz Eugen and the Bismarck? As it was, it was just a lucky shot that finally doomed the German battleship. Perhaps if it had been present the Prinz Eugen could have been the unlucky one. In any case, it would have been useful to force the British to divide up their meager air assets -- a total of 24 Swordfish were available between the two British carriers.