How many MM banks offer internships?

I'm currently going through the process of applying for summer analyst positions.  My main resource is obviously my career center, as I go to a target.  However, I would like to get my name out there to a lot of Mid-Market firms just to make sure I get an offer.  I have applied through the careers tab on a lot of their sites, but some of their sites don't say anything about careers and some have a "careers section" but don't mention internships.
Does this mean these companies probably don't offer internships?  Would it be worthwhile e-mailing each one of the with my cover letter and resume?  I'm just not really sure how common it is for smaller firms to offer SA spots.
Thanks

 

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