How does tracking a laptops IP work in free Wi-Fi areas?

I'm trying to understand how IP's work and all that as far as laptops goes. For a normal computer, if you connect to your internet, your IP can be tracked and it can be linked to you personally. On a laptop however, I would assume that it would be the same exact thing if you are connected at home.

If you are at a place with free wireless internet however, how does that work? Is it even possible to be traced? Can whatever someone is doing on a laptop be completely untraceable once they leave? If this is true, then I'm surprised I don't really hear of a lot of talk about illegal activity in free internet areas. It seems like it would be an easy way to get away with anything you didn't want to do at home

On a side note, I hope this isn't against any rules to ask this. I was just curious as to how it all works and the effects it may have crossed my mind. If I need to rephrase anything, just let me know.

most places that dish out free wifi will block out all ports except port 80 for web traffic and maybe 110 and 25 for email clients, game ports and ones that may be used for less friendly activities like torrent telnet ssh etc will be blocked for going in and out of the network.

legaly speaking, the activities on an internet line are the responsability of the line owner and not the end user can only speak for the UK on that)