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I want to send in a letter explaining why I want to go to law school (generally, not school specific). I'm sending in a LOCI as well. Is there a specific name and format/page length that the explanation letters should be?

Are you trying to send a letter to schools you are waitlisted for or are you talking about with your applications next year or what...? Regardless, this doesn't sound like a good idea. If you have something you really think is worth writing about, I would include it in an LOCI, not write a separate letter. Generally an LOCI should be about a page.