Olympus Mons once held this title outright. But in 1997, the Hubble Space Telescope discovered a huge crater on the asteroid Vesta. In 2011 the NASA space probe Dawn entered orbit around Vesta, and the crater was subsequently named Rheasilvia (after a mythological vestal virgin who was the mother of Romulus and Remus, the legendary founders of Rome).
The crater is 13 kilometres (8.1 miles) deep, and its diameter is 505 km (314 miles) – 90% of the diameter of Vesta itself. At its centre is a peak which is itself 200 kilometres (120 miles) in diameter at its base, and which rises to a height of between 20 and 25 kilometres (12 and 16 miles) above the floor of the crater. This makes it between around 2.5 and 3 times the height above sea level of Mount Everest (8.85 kilometres).
The height of Olympus Mons was measured by the Mars Global Surveyor spacecraft, between 1997 and 2006, as 21.9 kilometres (14 miles) – somewhere at the lower end of the estimated height range of the Rheasilvia peak. So "Vesta" would appear to be at least a valid alternative answer to this question.
To add further perspective, Mauna Kea and Mauna Loa on the island of Hawaii rise to a height of just over 10 kilometres from the ocean bed. Wikipedia lists five peaks on the Jovian satellites that are higher than this – the highest of them, on Iapetus, being around 20 kilometres – and three more on Mars that are between 11 and 15 kilometres in height.
© Haydn Thompson 2023