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I've noticed how the subject of OCs has been brought up quite a bit. I don't really have too much of a problem with OCs, so long as they're GOOD OCs. (which to me is the difference between OCs and fan characters. Character is decent/good= OC. Character is utter crap= fan character.) As long as they can effectively weave their OC into the story and not just have them appear out of nowhere and be like a God or something (i.e. rediculously powerful Pokemon, "has never been beaten", stuff like that), I'm good with it.
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Hope you don't mind me popping in, but I'm really interested in this concept. Do you mean Mary Sues/Gary Stus (which are a lot like what you're describing here, with ridiculously powerful Pokémon and god-like nature and all), or is "fan character" to you an umbrella concept that also includes Mary Sues/Gary Stus? Does the fan character concept cover flat, poorly developed characters in general (even if they're not Sues), or is it just limited to those inexplicably super-powerful ones?
Just in general curious because if this is a term that covers generally poorly written characters in fanfiction, that's a really cool concept. I don't think there's a term for it otherwise, so.