Which tools can track Bitcoin transactions and identify if they're received on Kraken, Binance, or CoinGate?

I run an test with this free tool, works well. My question is, if you don't have an address to go after it is impossible to find any wallet. Only if I enter my address I can see that for instant it is a kraken address or with another address it is indeed my cold wallet. So if I never give out my address to any person they won't be able to proof it is my cold wallet? if they find such addresses say in an kraken account together say with 60 or 80 other addresses they can't claim one of these are mine if I don't tell them?

Am I wrong here?
 
In the theory, yes they cannot prove it's your wallet, but I believe CEXs require to deposit only from your wallet address in somewhere of their ToS. Even if they don't, probably you are still responsible to explain SoF.

But Arkham is to track public wallet address, not private individuals.
 
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Yes, if you don't give out your newly created address, no one knows anything about it. Just make sure you take care of your IP as most wallets most likely spy heavily on you.

basically there's no way to prove a wallet belongs to xyz person even with forensics, its just a probability game which in the end can come reasonably close and reach over 90% easily. But at the end only xyz person can prove it by signing a message with his private key. This will be an 100% ownership proof which I would accept.
 
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