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Ok this might be a dumb question, but When You Apply to Law School is there like a box where you fill if you are applying for a scholarship? Or do they just give money to anyone they feel like giving if they have the grades and numbers? Are there any advantages of not applying for scholarship since they know you're paying full?

You apply for a merit scholarship when you apply to the school, generally.

I think some schools require you to check off a box that says you want to be considered for a scholarship.

NYU has a load of separate scholarships that you need to apply for. It is the only school I am aware of that has this.