As far as I know, nobody actually REPORTS any web activity to the authorities.
However details of your web searches is kept by Google (and other search companies), and details of web sites visited is kept by your ISP for a certain period.
I guess if the "authorities" suspect a person was involved in crime or terrorism then that would allow their web activities to be kept and used as evidence.
Windows keeps all sorts of information under the covers, often as hidden files, so I believe it would be VERY difficult to completely remove ALL evidence of web activity.
Even wiping your hard drive (with say a format) would not remove all files from the hard disk, and a simple recovery tool found on the web could "find" deleted files.
There are tools that can scrub a hard drive by writing "rubbish" over it over and over again, but on a large hard dirve that can take hours or even days to run.
There are ways of doing "secret" web activity (using a proxy I think or maybe other methods) but I have no details of how to do it.
I am sure someone can help you, or maybe search the web.