Shark finning is defined as the practise of removing a shark’s fins and discarding the body. It is still legal in New Zealand waters. It is illegal in Europe, Australia, the US and Canada.
Finning takes place on the boat, sometimes while the shark is still alive. Once the body is dumped the fishing vessel needs only to store the fins which are light weight, small and worth alot of $$$$ at $700(US) per kilo.
Finning a shark while alive is illegal in New Zealand waters but obviously its also extremely hard to prove. Check out the below video taken in the Marlborough Sounds in 2007:
Illegal live shark finning, Marborough Sounds New Zealand 2007