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Fanfiction has an extensive and devoted fanbase. There are a range of communities you can post your material on. Arguably the best-known and recommended of these is FanFiction.net. The website has an exhaustive list of different categories, genres and crossovers your work may fit into. Make an account and find the matching category for your work's source material.  Quotev, Archive of Our Own, and Wattpad are alternatives if you're looking to publish your story in additional places. It is recommended to publish your story on multiple sites if you can, as this will maximize your story's exposure. There are certain websites that specialize in fanfiction from a particular source. If you're looking to read or write fanfic from the Harry Potter universe for example, there is at least one website specifically dedicated to it. As a general rule, fanfiction should not be written with the intent of having it published commercially. Copyright protects unlicensed individuals from taking advantage of a creative property. However, publishers are beginning to warm up to the idea of publishing works of fanfiction. Although your choice of publisher will be limited to the one with the appropriate creative license, getting it accepted by them may actually stand the chance of turning your work into series canon, provided it doesn't conflict with established canon.  For fanfiction writers with commercial aspirations, you can remove any trademarked names and ideas in your story and replace them with original content. Some bestselling 'original' fiction, like E.L James' Fifty Shades of Grey and Lois McMaster Bujold's Vorkosigan Saga, began as works of fanfiction. If the book you're writing fanfiction for is common domain, it may be published without any name changes as long as your work is only based on the original works that are common domain. If you're starting to get serious about your creation you can do no better than to talk to other fanfiction aficionados. Sites like FanFiction are perfect for it. Not only will they be able to give you helpful tips and advice on how to improve your craft, they'll also probably help promote your work if they like it enough. As a general rule, if you offer feedback to someone's work, the chances are high you will receive feedback in return. It should go without saying that you'll receive the most helpful feedback from writers that are fans of the same source material you are using.

Summary:
Post your story on a Fanfiction outlet. Send your work to publishers. Link up with other fanfic writers.