Looking at this transaction I was wondering what the unspent part means. Does it belong to the original address owner? If so, how can it be used/claimed?
Edit: All cleared up, and seemingly a feature of Bitcoin-QT.
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The transaction in question has as input 0.37210663 BTC from address 1JvHotWuLtAU991q1mVsBJJe3SiLYq4LQD, and its outputs are:
The first output has already been spent. This means that whoever holds the private key for address 19ee... created a new transaction using this one as an input.
The second output has not yet been spent. This means that whoever holds the private key for address 1EXm... has not yet created a new transaction using this one as an input. They are free to do so at any time.
It is likely, but not certain, that one of the addresses 19ee and 1EXm belongs to the same person as the sending address 1JvH. Because the protocol requires that all coins from the input must be used in the outputs (or rather, any amount that is not used becomes a transaction fee), if the sender didn't actually want to spend all 0.372 BTC, they would have to send the remaining coins (minus whatever they wanted to offer as a fee) back to another address they control. This idea is called change. But there is no way for us to know for sure whether this happened, or if it did, which of 19ee and 1EXm is the "real" destination address and which one is the change address.
It is even possible that all three addresses belong to the same person, who simply wanted to split his coins among some new addresses for some reason. Again, we have no way to know.