Drowsing

[Jessica]

The act of semi-consciously [surfing the Internet], following [the rabbit] trail of link after link until you come back to reality only to realize you have [wander] far away from your original search.

[Justin Bieber]

When youre sleepily or absentmindedly [browsing] [something], [you are] drowsing.

[Julene]

Sleeping and browsing TV at the same time. You [doze] through the boring parts of games, but wake up and catch the big plays, [courtesy] of [crowd noise].