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As in, are there any firms that are more likely to respond to an unsolicited email than others?
Also, should you email someone or go through the application stuff on their website if they have one?

Not sure which firms - varies. I got good responses from Hogan Lovells, Weil, McDermott, and Perkins Coie.

I would send an email and simultaneously apply online, or wait to apply online until a response.

SullCrom will ding you by snail mail.

As a general matter, I don't think there are firms that are more likely than others to respond to massmail. If there were, word would get out and those firms would surely be inundated with applications from rising 2Ls

Yes - all the firms you haven't mailed yet.

Firms that don’t normally have summer classes are more receptive. I can’t think of one right now, but there are a handful of Amlaw firms that don’t have traditional programs but do take summers occasionally.