How much is public?

[Dabs]

How do they even know you went to a mixer? How does anyone know which address belongs to you?

Bitcoin is pseudo-anonymous, however, if you pay attention and do the right steps, it can be truly anonymous. It really is up to you how to apply it.

For example, it's not a secret that I control 1Dabsxxxxxxxx addresses. (not all of them, I mean, I can always generated a 1dicexxxxx address).

But how about all the other coins stores in all the other addresses no one else knows about, of if they do, it's only one or two people. And unless I sign a message using the private key, there is no proof that that particular address belongs to me.

You can prove an address belongs to you or is controlled by you.
You can not prove an address does not belong to anyone else.
You can guess that a person might control or own an address, but you can never prove it.

[nahtnam]

Well basically everything is public. Coinbase auto generates a address per transaction as long as its not to another coinbase address. If you want to check a balance of an address you can simple replace the address here: http://blockchain.info/address/18dHbkJbvmkqjtPMxukU6NQ8cuumRsDxXd

[odolvlobo]

But how about all the other coins stores in all the other addresses no one else knows about, of if they do, it's only one or two people. And unless I sign a message using the private key, there is no proof that that particular address belongs to me.

...
You can guess that a person might control or own an address, but you can never prove it.

In short, a wallet will combine addresses if it needs to. Thus, if you know that the address of one output in a transaction belongs to a person, you know that the addresses of the other outputs also belong to that person.

[Dabs]

Now, with CoinJoin and other 3rd party mixing services, you can't know for sure. Suddenly, you can only prove that that one address belongs to a person, but not the other outputs from different addresses, simply because it can all be combined and collectively signed, and it would appear that everyone owns all the coins or addresses in question.