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Last I checked,thread deletion is solely the province of site staff. Even then,they need a good reason. You can always fire off a PM to a member of staff,requesting a thread of yours (meaning,a thread you created yourself and are currently overseeing) to be deleted.
PMing a staff won't really get the job done, as the mod will advise you to place your request within the Roleplay Support. Just create a thread there with your request, and you should be good to go.
You should be able to delete your own thread as long as you are the creator of that thread. Just click Thread Tools in the upper right and the option should be there.