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Better clear up things with adsense people. They are helpful and set things right, in most sale purchase issues.
No, you should not.
You need to apply if you are buying a site where
adsense already implemented and you are not adsense publisher already.
photo200, that is incorrect.
You do have to re-apply if you were the original owner as well, and it was the site you used to sign up for. If it was simply a site you added after your original site, you just remove the AdSense script from the site.
Read seogrrl's experience here: [webmasterworld.com...] She had her account disabled when the new owners applied for AdSense and she had not reapplied for a new account.