IP Address Confusion

[Mr_Question]

As far as I understand, a laptop is assigned a different IP address for each different location it connects to (each different wireless network would assign a different IP address to the SAME laptop). A computer DOES NOT have a unique IP address unless it always connects to the same network.

If I connect to an open wireless network, say, at a hotel, is it possible for my download/upload activity to be tracked to my individual computer, or to me? Or can it only be tracked as far as having taken place at the hotel, and no further than that? Similarly, if there are multiple laptops at a single house with one wireless router, is it possible to tell which laptop did the downloading/uploading?

The RIAA typically busts people who download/upload at their own home, thus they might always have the same IP and are easily tracked. But if people do the deed from a wireless hotel internet connection, can they POSSIBLY get caught? If so, HOW do they track you? I'm not talking about plugging in to a cable in your hotel room, I am talking about open wireless networks at hotels, that may or may not require a password.

Please, constructive comments only (and only if you know some answers). I've Googled myself to death trying to find an answer with no luck. Thanks!