What happened to General Grievous's fighter?

Main canon

The last that's heard of the fighter is that it was used to transport Obi-Wan from Utapau to the Sundered Heart.

But Obi-Wan Kenobi killed the Separatist general before he could get away. After Obi-Wan was betrayed by his clone troops, he flew Grievous’s fighter to a rendezvous with Bail Organa and Yoda.

_{^{Star Wars: Databack - The Soulless One}}

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Legends.

The ship receives a further mention in Star Wars: The Life and Legend of Obi-Wan Kenobi. Obi-Wan disposed of it at a spaceport en route to Tatooine. It's not entirely clear whether he sold it or simply abandoned it.

R2-D2 had been to the Lars family moisture farm just prior to the Battle of Geonosis, and was able to provide the farm’s coordinates to Obi-Wan. The starfighter that Obi-Wan had taken from the late General Grievous had remained in Tantive IV’s docking bay, and Obi-Wan planned to use the starfighter to take Luke to a spaceport at Nar Shaddaa, a moon in a space sector controlled by the Hutts. As Obi-Wan carried Luke into the starfighter’s cockpit, R2-D2 beeped a farewell message to the Jedi. There was no point in Obi-Wan saying goodbye to C-3PO, for Bail Organa had already taken the security precaution of having the talkative protocol droid’s memory erased.   Holding Luke Skywalker’s swaddled form against his chest, Obi-Wan Kenobi sat in an uncomfortable seat on a crowded, Tatooine-bound starcruiser. The Jedi Master had little experience holding babies, but he did his best to look comfortable with the child in his arms.

Bail Organa had provided a supply of untraceable credits for Obi-Wan to pay for the journey to the sand planet. To further maintain secrecy, Obi-Wan and Luke were traveling to Tatooine via an indirect route starting from Nar Shaddaa on a series of public transports. During a layover at a space station, Obi-Wan witnessed a group of travelers at a HoloNet kiosk, watching a broadcast about recent events on Coruscant. Obi-Wan had cringed when he saw a hologram of Emperor Palpatine urging viewers to report anyone whom they suspected of being a Jedi or having “supernatural powers.” Palpatine’s words had prompted one traveler to remark, “Thank goodness those terrible Jedi were stopped!”

_{^{Star Wars: The Life and Legend of Obi-Wan Kenobi}}

It makes a further appearance in the Star Wars Galaxies expansion pack "Rage of the Wookiees". Evidently it was recovered by N-K Necrosis from a secret Empire storeroom on Utapau and used by this character until his death. At that point the deed transfers to the player character.