It is my understanding that any bitcoin address inside of one wallet can eventually be associated with any other addresses when coins are sent.

That said. If you take coins from wallet A and send them to almost any service that sents out payments in bulk for withdraw requests, this effectively anonymizes your coins in most cases. At this point all you need to do is withdraw to a wallet (Wallet B if you will) seperate from your original one and the coins should have few ties to the original.

Unless you tell someone or advertise or are found in possession of the private keys controlling a wallet there is no way to conclusively prove any particular individual owns any particular said address. Sending someone coins is effectively telling them you own that address.