Four times from nine attempts, the All Blacks have swept England, Ireland, Scotland and Wales at home, leaving them tied with South Africa but much better off than the Wallabies, whose sole success from the same number of Grand Slam tours came in 1984.
In 1963, a draw against Scotland denied Wilson Whineray's All Blacks, and again in 1972, Ian Kirkpatrick's men were thwarted by a stalemate with Ireland.
After five failed attempts, which included the 1905 Originals losing 3-0 to Wales in the only defeat of their 35-game tour, the All Blacks finally claimed their first Gram Slam in 1978.
The presence of a much-anticipated test with England at Twickenham next year - the first between the rugby heavyweights since 2014 - seemingly opened the door for a possible Grand Slam.
But New Zealand Rugby chief executive Steve Tew quashed such hopes, saying the All Blacks' next Grand Slam tour will not happen before 2020.
"There's certainly no chance of a Grand Slam before then," Tew told the Herald on Sunday. "Itineraries are set for '17 and '18, and [in] '19, there is a World Cup.
"We've agreed in the years beyond that there are opportunities for us to negotiate a fourth game that would give us a Grand Slam if we chose to pursue it and the nations we want to add are in agreement."
The decade-long wait between Grand Slam attempts will be the longest since the All Blacks claimed their first sweep. Three of their four successes were achieved between 2005 and 2010.
"It's one of those things that make a November tour a bit different and unique for players. From memory, we were criticised three or four years ago because we ended up with two or three shots at it and people said we were cheapening it, so there's an irony.
"I know the guys involved in those tours found it another tweak in the motivational tool kit."
• Tew was reluctant to discuss figures but, after selling 342,000 tickets to the 10 matches, the NZR could clear up to $40 million from the recent Lions tour.
Any such revenue will be spread across the next three to four years, and filter down through the game.
"We sold most of the seats we thought we would, so we should be in line for the income we've kept to ourselves and will continue to do so until everything is washed up."
Future Lions tours are slated to be cut to eight games and UK clubs, who control their players, are demanding a bigger piece of the pie. Tew believes the existing set-up balances inequitable revenue-sharing from the June and November test windows.
"We're not anticipating a significant change in the commercial arrangement in terms of the big picture. The good news is we have anchored the three next tours into the international calendar."
• From next year, South Africa has announced the Kings and Cheetahs will move to the Pro 12 competition as Super Rugby attempts to reduce from 18 to 15 teams. This scenario is conditional on the Australian Rugby Union finding a way to axe the Western Force.
With 350 professional players now abroad, rumblings continue that Europe may better suit South Africa. Tew remains confident they will stick with Super Rugby beyond the existing broadcasting deal which expires in 2020.
"The view we've got from our South African colleagues is Sanzaar remains their priority and preference, and they are committed to it. We'll be sitting down to map out our medium to long-term future very soon. That work has started, but has been put on hold largely given we need to be sorted for 2018 first."
• Debate continues about Eden Park's future as the Government and Auckland council squabble over who should foot considerable bills.
Projections suggest the stadium needs $250 million spent over the next five years. Tew said the NZR would not offer any investment, nor make the final decision on whether Auckland should push for another ground. A new central city stadium is forecast to cost around $1 billion.
"It still works fine from our point of view. The medium and long-term is a matter for all the parties that have an investment.
"It's going to require ongoing maintenance and reinvestment, and it's a matter whether that location is the best place to keep sinking that investment into, but that's a matter for Auckland city.
"We can inform the conversation by saying what it is we would do in various circumstances but it's pretty obvious in Auckland, with our biggest population and commercial base, there's always going to be an emphasis on big games in that city.
"Our guys have built up a track record at Eden Park [unbeaten since 1994] that is pretty special but, equally, people were quite attached to Carisbrook and Athletic Park. Whatever happens, we would respond accordingly."