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It sends it from the ClearCoin wallet. It doesn't do anything special to try to 'mix' coins, though, so if you send ClearCoin exactly 11 bitcoins and then release exactly 11 it is pretty likely the transaction history would be easy to figure out.
Which reminds me... I released a new version of ClearCoin this week that lets you release an arbitrary amount. So if you wanted to pay somebody 11 bitcoins but make it hard to figure out where the payment came from by looking at the transaction histories you could:
Fund the escrow account with, oh, I don't know, 20 bitcoins.
Release 11.
Let the escrow expire, and you'll be sent the leftover 9.