I just did a fresh install of Mountain Lion OS X version 10.8 onto a USB. The install takes 13.9GB of the USB after installation.
This was a fresh and basic install, no settings changed, literally a new, clean install with no preferences changed or anything. 13.9 GB is the final size on a 32GB drive.
The installation process itself was problem free on this 32GB drive. I would not use a 16GB drive to install Mountain Lion OS X on. The reason is because, even though the core installation of Mountain Lion OS MAY work, updates will not (because they require a download and you will have no space to spare). For this reason, I recommend installing the Mountain Lion OS on a 32GB drive, as minimum spec.
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