London-based IDC analyst Francisco Jeronimo said the S3 was likely to be one of the most sold smartphones this year.
Vodafone flew about 50 people to Sydney yesterday for the launch of the phone and 2degrees shows it can compete with its larger competitors by offering the phone on business and pay-monthly plans.
Stocks are limited, adding to the pressure for early adopters to have already ordered their phones through one of the carriers.
Samsung has created as much hype around the new Galaxy as Apple managed with the release of its latest iPhone.
But this time, Samsung is trying to overtake Apple as the main provider of smartphones.
The smartphone, running on Google's Android operating system has a 12.2 cm screen, one of the largest on smartphones ever, and much bigger than the display on the iPhone 4S.
Samsung said it expected the new flagship model to outsell its predecessor the Galaxy S2's 20 million sales worldwide.
The Galaxy S3 tracks the user's eye movements to keep the screen from dimming or turning off while in use.
In Europe, people were queuing to get the new phone, with some commentators likening it to the sale of the last iPhone.
Telecom chief market officer Jason Paris said the demand for the new phone both in New Zealand and overseas had been "remarkable".
However, early reviews from the United Kingdom have not been flattering.
Know Your Mobile writer Paul Briden said he took a look at the new phone at its London launch and left feeling disappointed and unimpressed.
The aesthetic design of the phone came across as fairly generic and uninspired.
"Samsung seems to be going full steam ahead and it was not a pleasant experience. Some of the extra features such as the 'pop-up-play' were nice, but the overall presentation ruins any appeal these additions might have brought to the phone. The end result is something we wouldn't be happy to fork out for with the hundreds of pounds typically associated with premium smartphones," Mr Briden wrote.
