Say someone were to use a free wireless internet connection provided at an apartment building. They just give you a password to connect to it. And if that person were downloading copyrighted material such as movies, music, games, etc is there any way to have that traced back to that person by the government? I mean they should only be able to trace it to that particular apartment building but have no idea who exactly right?

Oh aren`t you a slyck one.
But then if the network owner fails to even consider preventing this , they may easily be held accountable i guess . Anyway , i`d say this is a

If someone is given an account on a network then all that account's activities could be logged and traced back to the account holder. Even simple routers may have logging capabilities that would give time and IPs connected. If someone has root access to the network appliance and can use that account or make a new one that isn't easily traceable to their computer, then ...

I would think you'd also have to spoof your MAC address. And you'd have to rotate through several addresses. And even then you could be discovered by the process of elimination.

Someone might use a directional antenna to use the free wireless internet connection provided in a different apartment building than the one they lived in and that would make the search for them more difficult. But not impossible.

I envision a PHORM-like packet monitoring contraption at the ISP. It could tell, down to the millisecond, when the MAC was changed. If any other traffic (think email) was "personally identifiable," well there you are.

I would not count for a "wireless internet connection" providing much in the way of anonymity.
--CF