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From Tor:

"So I'm totally anonymous if I use Tor?

No.

First, Tor protects the network communications. It separates where you are from where you are going on the Internet. What content and data you transmit over Tor is controlled by you. If you login to Google or Facebook via Tor, the local ISP or network provider doesn't know you are visiting Google or Facebook. Google and Facebook don't know where you are in the world. However, since you have logged into their sites, they know who you are. If you don't want to share information, you are in control."