We've already shown you how to use Virtualbox to install Mac OS X Snow Leopard and Mac OS X Lion on virtual machines in Windows, since it's great practice for installing Mac OS X on your actual computer. And now that OS X Mountain Lion 10.8 has been officially released, we can finally demonstrate how to do it with Mountain Lion too.
LATEST UPDATE (January 27, 2013): Don't want to use Hackboot? Check out the simpler iAtkos method for installing Mountain Lion on Virtualbox instead.
In essence, this method will let you run Mac OS X from inside a program window in Windows. As always, we're going to use Virtualbox for this. It's important to note that Windows virtualization programs do not "officially" support Mac OS X, so you will not be able to enable full graphics support. This tutorial should only be taken as a proof of concept.
You need a computer with Windows to run Mac OS X on Windows (of course). The "System Type" of your copy of Windows needs to be 64-bit, because OS X Mountain Lion is a 64-bit operating system. If you have a 32-bit copy of Windows, you can only install Mac OS X Snow Leopard on Virtualbox. You will need at least 4 GB of RAM and a dual-core (two core) processor or better. Personally, the computer I was using for this had a 4-core processor and 12 GB RAM, which is way more than enough. You also need about 10 GB of unused hard drive space.
Right click on "My Computer" on your desktop and click "Properties" to check the stats on your computer. If it doesn't directly tell you how many cores your processor has, look up your processor model on Wikipedia or Google. You also want to find out whether your processor is made by "Intel" or "AMD". Computers with AMD processors will not work with Mountain Lion.
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