I asked this same question recently, and was informed that the information (if any) would be contained on the one computer used at the time, it would not share the information between the two computer's.
So if that is the case, then make sure the hard-drive is cleared of any information before you give it away. Consider though, that with the right equipment or program, information from an hard-drive could be retrieved by anyone determined to gain this information. Sure way of getting rid of information is to destroy the hard-drive completely.
If the information on the hard-drive is not relevant, then CCleaner might help with a clean?.