I always find it very creepy when I looked something up on someone else's laptop and use it again half a year later, only to find that it remembers my last visit and (for example) centers the map where I last left it. I'm so used to having things be cleaned up against tracking, I don't even really experience what the web is like these days.
Or can it?
That just leaves hiding the tab bar, gestures that work in all windows (e.g. also in the view-source URL windows) and that work before the target page has loaded, etc.