Back in 1996, the Dome was a red pen squiggle, a notion. Then, the site chosen for it, the Greenwich peninsula, was a derelict, 300-acre expanse of contaminated land. In the early days of the Millennium Commission, the first body set up to plan celebrations to mark the year 2000, nobody had a clear idea of what to do. When an exhibition was first suggested, the commissioners were split. Michael Heseltine wanted it, and so did the former Times editor, Simon Jenkins. The rest didn't. Even Hezza and Jenkins couldn't agree; the politician wanted a trade fair, Jenkins thought the emphasis should be on fun. But by then, the bureaucracy was spawning. There were already 60 "expert" advisers, yet still no vision.
The first chief executive, a former boss of the charity Save the Children, stayed for one day. Even before Nicholas Hinton's arrival he tried to appoint a friend as his deputy and buy pounds 1,000 leather chairs for his office. The commissioners sacked him. Mr Hinton was not the only man to go. Gary Withers, the boss of Imagination, a design company, who was so influential in the early days of the Dome's design, quit, bitter and broken, after battling for months to try to get his plans accepted.
Then there was the German company, whose PVC roof for the Dome was exposed by the Independent on Sunday as toxic. After threats from Greenpeace to occupy the site, the firm was thrown off the job.
One of the earliest rows was over Mr Hinton's successor. When Stephen Dorrell, then Secretary of State for National Heritage, tried to appoint Jennifer Page, chief executive of English Heritage, the corridors of Whitehall rang with the raised voices of its chairman, Jocelyn Stevens, and Hayden Phillips, permanent secretary at the department, both determined to have her on board.
Ms Page has been one of the most formidable operators in the Dome's history. There was no sense that the public wanted such a building; it was a political notion - and the public would get it, funded by their own money via the National Lottery. Ms Page pushed the project through crisis after crisis, first running the Commission, and then the private firm, Millennium Central, (later called New Millennium Experience), which was also a public body subject to government rules.
She has had to contend with the commissioners, with John Major's Millennium Committee, the special Cabinet Home and Social Affairs Committee, the Litmus Group, formed to consider creative issues, the appointment of zone "godparents", the Millennium co-ordinating group, and an assortment of government ministers, including Peter Mandelson and Lord Falconer.
And there have always been three near-insurmountable problems with the project: the unmoveable deadline, the commercial performance, and public accountability. There was little that people involved in the Dome agreed on except location. Greenwich, with its connection with time, via the meridian line, was an obvious choice. The Greenwich peninsula site, owned by British Gas, was, in its polluted condition, worthless, so no property developer wanted it. Despite the convention of "let the polluter pay", British Gas engineered a deal to sell it to the government for pounds 20m -- exactly the same amount it had agreed originally to invest in the Tube's Jubilee line, whose arrival at Greenwich would have inevitably boosted the value of British Gas's landholding.
The utility was well aware of the potential of the peninsula - it being close to the revived Docklands. It called in the architect Richard Rogers, who with his partner, Mike Davies, had long worked on regeneration of derelict urban sites. At this stage, Mr Rogers was also involved in secret meetings about the Millennium with people who had the ear of Labour figures - such as David Puttnam, Melvyn Bragg, Michael Grade, Alan Yentob, Maurice Saatchi, former Kinnock speechwriter John Newbigin, and John Sorrell, chairman of the Design Council. Later they joined forces with Lord Hollick and Harvey Goldsmith to become M2000, the body behind the Dome's design.
The most testing time was from December 1996 to June 1997. The Conservative government was in its dying days, and the Dome was in danger of becoming becalmed in the pre-election political doldrums. It needed commitment from both Labour and Tory politicians if it was to secure private sector finance. Costs were rising fast, the budget rose to pounds 800m but the Commission's grant would never be enough. Extra money came from the lottery, a new company was formed to run it, and Ms Page was made chief executive.
Twice Tony Blair came close to killing the Dome. Once, before the election, Mr Heseltine went cap in hand to get a commitment from the prime minister apparent. Mr Blair, in turn, got the Tory deputy prime minister to concede everything Labour wanted - a full review in government and an unchangeable lid on the budget. In government, the new Cabinet had to decide finally whether or not to give the go-ahead. The politicians were still split. The Chancellor, Gordon Brown, thought it too costly; others thought it would epitomise Blairism being unifying, progressive and optimistic. In the end, with just minutes to go before a crucial Dome session, Mr Blair again made a commitment. What convinced him? What made the difference?
It was, eventually, to do with power of a very particular kind - the power of children and of sentiment. The government is young, with many members only just growing into middle-age; some of them have children, and they are of an age to have been children themselves in 1951, the year of the Festival of Britain. It was Mr Mandelson's grandfather, Herbert Morrison, who was responsible for that post-war celebration of hope for the future.
They may have recalled its excitement, its sense of a new beginning after years of rationing and austerity during and after the war. Could that buzz happen again? Mr Jenkins thought so, as he told the Prime Minister in a missive that has gone down in history as "the Euan letter". It was Mr Jenkins's description of how the the Dome and the millennium festival would only succeed if it offered something to Euan - "such events are milestones in a nation's history, but also a child's life" - that really convinced the Prime Minister.
In five days, we shall see if the Dome has succeeded; whether it will be for Euan Blair and millions of other children a building and an experience they will remember for ever.