According to quite a lot of comparative planetary geology work, Mt. Everest, Mauna Kea, etc. are pretty close to the height limit imposed by gravity and structural strength. On some objects (like Mercury or the Moon: see https://arxiv.org/pdf/1511.04297.pdf) there aren't any mountains high enough to hit that limit, but Earth seems to have active enough tectonics to push up at that limit despite weathering.
A bit of one, a bit of the other, AFAIK. Of course, having geological weathering is also a function of gravity; small objects don't have the atmosphere for it.
The tallest planetary mountain in the solar system is Olympus Mons on Mars, about 2.5x as tall as Mount Everest (as measured from sea level). This is only possible because Mars has 1/3 the gravity of Earth.
