What happens when a coin is split? The original Bitcoin paper states:


  We define an electronic coin as a chain of digital signatures.


What happens when a coin is subdivided and transferred to multiple owners? Does each coin fragment form its own chain of digital signatures, or are all the fragments still part of this one original chain of digital signatures?
Each fragment starts it's own chain.

Edit: I randomly selected a transaction for you to see.  Try this link: http://blockchain.info/tree/7514743 and click on the yellow circles.

Edit2:: Actually, this one is more interesting: http://blockchain.info/tree/50429084  In the former, the payments mostly returned in part to the original address.  That's odd.  The usual way of doing things is sending to one address and returning to yourself at yet another address.