Plankton's plan is to obtain King Neptune's crown and frame Mr. Krabs, in which the punishment would be execution. As Mr. Krabs is frozen at first by Neptune, and with SpongeBob and Patrick on the journey to Shell City and Squidward enjoying his time off, no one is able to protect the secret formula, so Plankton steals it and put the Krusty Krab out of business as a result.
Customers come to the Chum Bucket, in which he uses bucket helmets to mind control them. He rules Bikini Bottom and renames it "Planktopolis." However, it is foiled by SpongeBob and Patrick making it to Shell City and back, and then Plankton is arrested, Mr. Krabs is freed, and Neptune gets his crown back.
"Plan Z" is also the name of Adolf Hitler's plan for rearming the German Navy prior to World War II (Kriegsmarine) so that it could match up with the British Royal Navy on equal terms (the Kriegsmarine was a weak navy during Hitler's time). Unfortunately, war broke out in 1939 before the plan could be completed (theorized to be finished in 1947), and it fell apart in three years.
A second Plan Z was formed in 1973 as a military coup to topple Chilean president Salvador Allende, though this was shown to be a fake as revealed by the CIA in 1999.