First, let me say that all shows are different, so the "who to pitch to" is on a show to show basis. Which is why one good resources is
1. To get TV writer/producer mentors if you don't know how to get a mentor check out The Greenlight Mentor Program.
Here are some more ideas:
2. Through an agent if you have one, who has a relationship with someone on the show.
3. Through referrals from people you know to the people they know who work on shows. Now keep in mind that many writer/producers can't listen to unsolicited pitches because if they come up with a similar character they don't want to be sued.
4. Write a spec script for a DIFFERENT show, using the character you created. So find a show and write an off beat spec that includes your character. The reason I say write a script for a different show is because, if you write a spec for their show, they most likely won't read it. But if you write a fantasy SMASH where someone trips on payote and has a "musical vision" with your character in it... could be cutting edge... or could be lame like the Glee induced Grey's Anatomy Singing episode GAG! So get some feedback from good writers before submitting it.
5. Create a video blog or webseries about your character.
Now, as far as the worst thing you can do: Be unprofessional. No one wants a "stalker" or someone who hasn't done their research. Don't send unsolicited material. Don't do 'crazy antics' to get attention, while it's important to take risks, they should be calculated risks and representing yourself in a way that gets a producer's attention as someone he/she wouldn't want on their set is not good. Do not show up at their house or production office in your costume and start performing. Note: these are my opinions. You may hear a cooky story about someone who dressed up in full knight armor and got a job on a period piece, but these stories are 1 in a million, and I don't coach to those odds.
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