sleepsurfing
Surfing the web while effectively asleep.
I was surfing te web for one thing, when I finally woke up from my 'sleepsurfing' trance, I was on a site that was completely foreign to me with no idea how I got there.
sleepsurf
To surf the web while effectively asleep, or so tired you aren't completely aware of where you're going. As one would sleepwalk.
"I finished studying for the exam, got some hot chocolate and read my email, then proceeded to sleepsurf the net until about 2am."