"It's not done this way anywhere else in the world. It's a really impossible job in many ways," Mr Brown said.
In a statement, Mr Quigley said his job was mostly done.
"My job was to lay the foundations for the NBN for the next 30 years. That job is largely complete. NBN Co is now a well-established wholesale telecommunications company with a nationwide workforce, delivery partners, infrastructure agreements, complex IT systems and more than 40 retail customers which are supplying fast, reliable and affordable broadband to a growing number of Australians."
"The role of the next CEO will be to build on these foundations."
NBN Co Chairman Siobhan McKenna said the company's directors "were proud of Mike's achievements and welcome his decision to remain in post to ensure a smooth transition to his successor."
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