Open Question: What happens if Someone uses Wi-Fi to illegally download copyrighted content?

I'm sure it happens on trains at Heathrow etc... but what if one downloads copyrighted material like a new movie or a new game. Would the authorities be able to trace you? Does Wi-Fi allow pirates to get away with these serious crimes? I ask this because to my knowledge the authorities Ip address to track down pirates and with wi-Fi isn't the Ip address unknown as it is on a public network?