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Alright, so I have been speaking to a number firms in my area, and a few have asked for a resume. This might be common knowledge, but should I give him my CV and resume, or just resume? I'm thinking that if he wanted the CV he would have asked for it, but I don't know if it is common practice to submit both to firms.

You should send a one page resume. They may also want a cover letter, transcript, and writing sample at some point.

A CV is more of an academic thing. Have a 1-page resume that you update during law school.