I don't know about browser history, but there's evidence that Google use your user-agent string other connection details to uniquely identify you when you conne

I don't know about browser history, but there's evidence that Google use your user-agent string other connection details to uniquely identify you when you connect to their servers, and to build a history of your search terms even without you having a google account. They can later use that knowledge to serve directed advertising in search results across any of their products.