It anonymizes by taking it in from one wallet, combining it with bitcoins from other accounts, and then returns it to another wallet you control.
so it is known what addresses paid in and paid out of the pool.
If you wanted to hire a hitman the state would know that you bought that $10k of BTC, and they would see that $10k of BTC go into a pool. They would see the hitman paid out of that pool (maybe with another hop). So the paper trail would have a break in it, but could kind of get tied to you.
You need to do face to face with someone you don't know, maybe with a 3rd party to escrow, that's really the only way.
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