Quote from: HNajafi on April 04, 2021, 07:18:13 AM

What mechanism for proof unique public key when creating a wallet happen with several sources(such as "wallet.btc.com" ,"wallet.bitcoin.com", "www.blockchain.com/wallet" and... )?

There is no 'mechanism' behind it because no mechanism is needed, imho.
As previously stated, the process of creating a private/public key is so complex that the theoretical possibility of collision exists only as a mathematical probability and is practically equal to zero.

However, I agree with Coolcryptovator. A much greater risk is the credibility of the service and/or software you use to generate bitcoin addresses. If the software is open-source, you can be confident that hundreds or thousands of developers and programmers have already tested it, while with closed-source services, you have no idea what's going on under the hood.