What's the maximum height a mountain can be on Earth?

 

Mountain height is a combination of geologic forces reduced by gravity and erosion.

 

 

No, say we have an early Mars-like world with just enough mass and water to develop plate tectonics, but not enough water to erode the mountains too quickly. How tall can they get? ten miles? thirty miles? etc.

There is another issue called isostacy that needs to be considered.

 

See http://en.wikipedia.org/wiki/Isostasy

 

Basically the earth is not rigid under the continents and that as mountains increase in height they 'sink' down.