Well the driver will take up very little hard drive space depending on the video card. Now all video cards have built in memory (RAM) but after the ammount that is on the video card runs out. It will start using the RAM on your computer. Just depends on the game you are trying to run. Also your Proccessor, RAM and Video Card all work together for running games. Hope this helped :)
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Video/graphics cards do contain memory of their own, but they are not memory in itself.