Let's suppose you bought 10k USD in bitcoin in Coinbase, and you sent your documents there and withdrawal those funds to the address A.
You can just send your coins to a bitcoin mixer (address B), and then the mixer will send you back other coins (which are not linked to your coins from address B) from address C to your address D.
This way you can achieve some anonymity.
Is it theoretically possible to untangle this chain? address A-B-C-D and so on.
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For common users, if you have a low amount (not thousands of btc) you can get "clean " coins, not attached to you.
You can send 2 Btc to a mixer, For example, and receive several small amount of 0.02 or 0.05 btc, which were never linked to those 2 btc you had. Those small chips come from other addresses, those are other coins. Then they are not linked to you.
As o_e_l_e_o said, large amount make jt Harder to mix and someone may break it easier.