What is the tallest mountain possible in any gravitational environment?

In world building it is often interesting to consider extreme landscapes "“ how tall can a mountain be on Earth for example. But what is the tallest mountain possible in any gravitational environment?

Formation of the mountain may be unlikely in the extreme, but it must be at least theoretically possible to form by natural processes.

For the purposes of this question a mountain's height is the distance between the mountain peak and the average radius of the object it is physically joined to.

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What is the tallest mountain possible in any gravitational environment?

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