"What If General Grievous Survived?"

                                    

                                              
What if General Grievous survived his battle on Utapau? What if Obi-Wan was unsuccessful in killing him, and he escaped? This "What If" can go two ways, if Obi-Wan died to General Grievous, which I can't see happening due to his mastery (and often being called The Master) of the defensive form of Lightsaber combat known as Soresu (form 3). We can also go if General Grievous just successfully escapes as he often does.

General Grievous would flee to Mustafar, where Palpatine told the Separatist Leaders to go. Kenobi would inform the council of his failure, meaning that the Clone Wars would rage on--not for long, however. Despite Grievous successfully evading Obi-Wan, Palpatine will still go through with coercing Anakin and ordering the Jedi to be killed. It is an unfortunate setback that Grievous lived to Palpatine, but he had full confidence in Anakin's ability to kill him. Confidence, as Yoda says, is misplaced. Order 66 is enacted, Jedi are wiped out, the events play out generally the same.

Anakin is ordered to go to Mustafar to deal with the Separatist Leaders. Now, he would have to face General Grievous. Grievous would meet Anakin as soon as Anakin got off of his ship. Anakin would be unable to defeat Grievous, as Obi-Wan could've. As I've said earlier, Obi-Wan is a master (if not The Master) of Soresu, a defensive form of defense. Anakin and Grievous are both aggressive attackers. Grievous knowing Makashi and Anakin knowing Djem So.

Grievous would use his escape tactics and evade the newly appointed Sith Lord, meanwhile the rest of the Leaders are slaughtered, like in the original timeline. Everything plays out the same, Anakin loses to Obi-Wan, Yoda fails to kill Sidious, and Luke is born. Grievous, still a leader & rally cause for the Separatist movement will try to rally the rest of the droids and go underground. He could either do two things from here on out; help the Rebel alliance or start havoc in his own way. I believe that either way, it will come to one conclusion, the same fate.

He will die by either Vader's or Sidious' hand. He would be a priority target for the Empire and would be on top of their kill list. Whether when it happens, it is up for debate. However, Grievous is rash. It will be sooner than later. If Grievous didn't die in Revenge of the Sith, he would've died between the 18 years of A New Hope and Revenge of the Sith timeline. Either by Stormtroopers, Darth Vader's, or Sidious' hand.