Three of its five directors are appointed by Fairfax, and that is not expected to change.
But Trade Me chief executive Jon Macdonald said that the initial 34 per cent float distanced the company from Fairfax and meant it related to the rest of the market more independently.
Former Fairfax chief executive David Kirk - now chairman of Trade Me - drew a mixed reaction when he bought Trade Me for A$700 million in 2006, but the float of 34 per cent of the company last year raised A$364 million.
The latest 15 per cent raised A$160 million, a total of $524 million for selling 49 per cent of the firm.
Meanwhile, Fairfax, which takes one-third of its non-Trade Me revenue from New Zealand, announced a big restructuring of its Australian assets owing to the growing shift of advertisers to digital media.
However, Fairfax insists that the major upheavals across the Tasman will not happen here, because readers' switch to digital has been slower here.
Fairfax New Zealand chief executive Allen Williams said there were no plans for job cuts in New Zealand.
The main effects of the restructuring, which will mean the loss of 1900 jobs over three years, were on metropolitan newspapers such as the Age in Melbourne and the Sydney Morning Herald.
Williams said Fairfax was proceeding with regionalisation of the Sunday Star-Times newspaper after July 1.