Sj often takes an office laptop home. He wants to know if "the System admin from my office" can see what websites he visits at home.
Virtually all browsers these days have private modes (Chrome calls it Incognito Mode). In this condition, the browser doesn't keep records of where you've been. In theory, and often in fact, you can use these modes and leave no trace of where you've been. (I've discussed these modes in more detail last April.)
But the chance that a private mode will protect you drops considerably on a company computer. It's quite possible that this computer contains software that tracks everything you do on it. (If you're a parent, you may be using similar software to track your kids' browsing habits.)
[Have a tech question? Ask PCWorld Contributing Editor Lincoln Spector. Send your query to firstname.lastname@example.org.]
Remember that this is not your computer. It belongs to your employer, who has a legal and (in my opinion) moral right to know what happens on it. The company could lose huge amounts of money from a malware attack, and therefore has good reasons to limit what you can do with Internet-connected company property.
But whether your employer's rules make sense or not, you have to follow them. And unless you've been explicitly told otherwise (and maybe even if you have), you should assume that your office PC is spying on you, at the office and when you take it home.