Palpatine then tells Anakin to kill Dooku on the spot; after initial hesitation, Anakin brutally decapitates Dooku, an act that sets off a chain of events that leads to Anakin's fall to the dark side and transformation into Darth Vader.
Palpatine then tells Anakin to kill Dooku on the spot. Anakin brutally decapitates Dooku. This is after initial hesitation. Dooku is an act. This act sets off a chain of events. These events leads to Anakin's fall to the dark side into Darth Vader. These events leads to Anakin's fall to transformation into Darth Vader.