What information about the client is transmitted to the host of an SSL connection?

I know the IP address and browser information of visitors is recorded in the server logs of Web hosts, but what is additional information, if any, results from an SSL connection? If I visit an https site, what information is or can be recorded by the server hosting the secure connection?

It depends. If the site is using a cookie, then it can get pretty much any info it wants...

In typical end-user/browser usage, TLS authentication is unilateral: only the server is authenticated (the client knows the server's identity), but not vice versa (the client remains unauthenticated or anonynmous).

P.S - SSL is now TLS.