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Say I give 1 BTC to Alice who gives it to Bob who gives it to Carol. Can I now figure out that my original BTC is now with Carol? Of course, by Carol I mean an anonymous address.

I'm thinking of a reverse wheresgeorge.com where I can trace where a BTC I owned went. I presume this is not possible otherwise hackers would never be able to keep stolen bitcoins.

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Actually, yes, this is possible. However, your payment output might get split or combined with other payment outputs in later payments. Therefore, the graph will be less linear than you suggest:

    C ↴       ↱ H
A → B → D → E → G
          ↳ F

So, A would be sent to B, then B + C would produce D, D would be split up to E and F, E would further be split up to G and H. B would be a 100% child of A, D, E, F, G and H only 50% (if A and C were the same size).

This would get much more complicated over time where many outputs get combined and split and so forth, but you could actually continue to track this forever. The issue is actually not with the tracing of funds, but with the proving that funds were indeed stolen. If you are more interested in this, you might find this related question useful: What are tainted coins exactly?

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