The Bell 206 JetRanger helicopter crashed into the water moments after takeoff, about 20m from the helipad.
A New York Police Department spokesman said the helicopter had apparently run into trouble after takeoff and the pilot, Paul Dudley, was trying to return to the helipad when it crashed.
While investigators looked for clues to explain why the private helicopter crashed into New York City's East River, some New York politicians called for a ban on tourist and what they called "non-essential'' helicopter flights in the city.
A member of the National Transportation Safety Board, Mark Rosekind, said the privately operated Bell 206 likely did not have a flight data recorder, but engine monitors and Global Positioning System navigation equipment may have stored useful information.
Family rush to US
Ms Tamaki's mother and sister Milly are expected to fly to New York today.
Her other sister, Suzanne Tamaki, a Wellington artist and jewellery designer, said last night: "We don't have much information, but we managed to speak to a doctor over there ... My sister is in a critical condition. She has stabilised but they're waiting for 24 hours. "They're worried about brain and lung damage."
Suzanne Tamaki said the family were devastated by Ms Nicholson's death.
"She's basically our sister-in-law. We all loved her. Our hearts go out to her family."
She found out about the crash when she checked her Facebook messages yesterday.
"An old school friend sent me a message and said, 'Oh my God, have you seen the papers?' I didn't know what she was talking about. It was on the front page of the Sydney papers ... before the family had even been contacted.
"It's been really hard for us seeing the images on TV and on the internet."
Helen Tamaki works as an IT operations manager for a company called Salesforce and has lived in Sydney for about 20 years.
"She's doing really well over there. She's a really awesome businesswoman," Suzanne Tamaki said.
The survivors were plucked from the river by emergency service workers.
Two were clinging to the helicopter's skids shouting "help us" as they tried to stay above the water.
Witnesses describe crash
Limousine driver Mike Pratley was on a pedestrian walkway near the helipad when the accident happened.
"It lifted up, and it never really looked right ... It was out of control," he told the New York Times.
Jose Reyes said the nose of the helicopter bobbed up and down before the machine plunged to the water. "I saw the helicopter start to spin, and then it went down. Three seconds, then boom."
Joy Garnett said the chopper was about 7m off the ground when it dropped into the water and flipped over.
She said people on the dock started throwing life jackets and buoys. Two people came up out of the waves.
Carlos Acevedo said: "It sank fast. In seconds. Like the water was sucking it in."
New York Mayor Michael Bloomberg gave his condolences to Ms Nicholson's family. "It is a sad day."
Ms Nicholson previously owned the Madame Fling Flong bar and Sonia's restaurant in Newtown, Sydney.
Investigation continues
Investigators said they had collected video of the crash and were studying the weather conditions.
A weather reporting station at nearby LaGuardia Airport had reported gusts of up to 32 kph around the time of the crash. Winds can sometimes be rougher along the river because of turbulence caused by tall buildings and bridges.
National Transportation Safety Board member Mark Rosekind said a piece of one of the helicopter's main rotor blades was missing, but it's not clear whether it broke before or after the crash.
Meanwhile, a portrait emerged of the pilot as an expert flier who in 2006 landed a plane in a New York City park after its engine failed. No one was hurt.
Mr Rosekind said Mr Dudley had more than 2,200 hours of flight experience, including 500 hours in Bell 206s. The Bell 206 Mr Dudley was flying was built in 1976. Mr Rosekind said investigators would review its maintenance records.
The crash has prompted politicians to call for a ban on tourist helicopter flights over the city.
Congressman Jerrold Nadler and five state and city legislators said they want to cut down on air traffic but had not decided how to enforce such a ban.
The Bell 206 Jet Ranger is one of the world's most popular helicopter models. They are light and highly manoeuvrable, making them popular with television stations and air taxi companies.
The East River has been particularly tricky for pilots because of its many bridges and its proximity to LaGuardia, one of the nation's busiest airports.
Mr Dudley filed a lawsuit against a proposed heliport in Kearny, New Jersey, after a deadly collision in 2009 between a helicopter and a small plane over New York City's Hudson River, citing safety concerns.
He argued that additional planes flying over Jersey City, New Jersey, on their way to New York would create dangerous air traffic, the Newark Star-Ledger reported at the time.
