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For me, the result is this: "Based on the central character in the Eminem song of the same name, a "stan" is an overzealous maniacal fan for any celebrity or athlete." Close enough, although I'd replace "celebrity or athlete" with "electronic gadget or video game."
Just like most other Facebook trends, this one seems equally useless (other than being a nice promotion for Urban Dictionary), but it can be a lot of fun. If you decide try it out, be careful, Urban Dictionary is a site that doesn't shy away from very strong language.
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