GrooveShark AMA on Reddit
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They struck a deal with EMI very early in the game and the other labels followed suit.
Source: http://www.thetechherald.com/article.php/200943/4665/Grooves...
As far as I understand, basically the same way YouTube and
Vimeo are: DMCA safe harbor laws, plus paying streaming
royalty boards etc. We're also trying to get direct deals
with all the majors too, but those negotiations take a looong
time. It was a couple years just to get EMI signed.
So it looks like they only have an EMI deal right now but other labels are in progress.