No Australian city has experienced growth on this scale before. The closest thing in the past was 50 or 60 years ago, when Melbourne and Sydney were the dual epicentres of the post-war boom in European migration, boosting each city's population by up to 75,000 a year. That migration boom became a transformative experience: it changed not only the scale of the two cities, and their problems, but also their food, their culture, and their sense of themselves.

In those 25 years, Melbourne grew from a city of 1.2 million to one of 2.6 million. If today's Melbourne were to grow for 25 years at the pace it has over the past decade, let alone the past year, by 2042 it would have 8 million people. That, too, would be a very different city.

Apart from the first years of World War II, when it became the defence headquarters of a nation at war, Melbourne has never dominated Australia's population growth like this. Last year this city's population grew by 2.4 per cent – twice the pace of the rest of Australia, which grew 1.2 per cent.

Of the nation's 30 largest cities, Melbourne was also the fastest-growing. Geelong was second, growing by 2.1 per cent; Ballarat was fourth, Bendigo eighth, and Albury-Wodonga ninth. Only four cities outside Victoria – the Gold Coast, the Sunshine Coast, Brisbane and Sydney – even kept up with the nation's population growth rate.

Once again, migration is driving the city's growth. But the migrants of today are coming from different places, for different reasons, through different channels.

And right now, what is happening is different from what policy makers and analysts had assumed was happening: high immigration and population growth roughly spread across the nation, or at least across the four biggest cities. But now, in most of Australia, population growth and immigration are back to average levels.

In effect, three in every eight new residents of Australia are settling in Melbourne or inner Victoria – the region within 150 kilometres of the city. We are taking 37 per cent of the nation's population growth.

In the year to June, 138,000 migrants settled in Victoria, permanently or for the long term, while 73,000 Australians, former migrants or temporary residents, left. That meant the state took in a net 65,000 migrants from overseas – fewer than New South Wales (71,000), but in net terms, NSW lost 11,000 of its own people to interstate migration, whereas Victoria gained 17,000. Net result: Victoria gained 82,000 migrants, NSW 60,000.

It's a gear change in a migration boom that has already transformed the city. In just 15 years, Melbourne's population has grown by a third. The Bureau of Statistics estimates that in the 10 years to June 2016, the population of greater Melbourne grew by 880,876, or 23.4 per cent. In a decade, the city added almost a quarter to its population.

We are now experiencing a second wave of large-scale migration, primarily from India and China. It has brought gains and losses: new skills and demands for our services, but also more crowding of the city's roads, trains, and public services. And this wave of high immigration is likely to continue long into the future.

Another new development is worth noting. Victorian women until recently had fewer babies, and had them later, than women in the rest of Australia. But Victoria now has an outsize share of gen Ys in their 20s and 30s – and in 2015-16, its birth rate was the highest of any state, and its rate of natural increase (births minus deaths) second only to Western Australia. That glut of gen Ys suggests there will be a lot of babies born here in the next 20 years – and that will increase the height of the new wave of population growth breaking over us.

Demography is destiny, the old saying goes. But demography is also about density. And that is one of the ways the new wave of immigration is changing Melbourne.

It's been a long time coming. The planners of the old Melbourne and Metropolitan Board of Works weren't thinking about this massive influx of migrants in 1981 when they amended the city's planning scheme to encourage urban consolidation.

Nor were John Cain and his government when they developed Southbank and brought housing into the city. And early in the Kennett government, when Victoria experienced three years of net out-migration to the rest of the world, who would have anticipated that within a generation, we would be experiencing net immigration of 82,000 people a year?

But we have, and in the past five or 10 years, urban consolidation has provided almost half the new housing needed to meet the city's population boom. The Bureau of Statistics' estimates imply that between 2006 and 2016, the population living within 10 kilometres of the GPO grew by about 200,000 or 24 per cent.

The population of the city of Melbourne alone shot up by 56,182 or 70 per cent. And by 2016 every single suburb within that 10-kilometre core had more people living there than they had 10 years earlier.

In Abbotsford, the population almost doubled, from 4537 to 8110, as new apartment blocks rose over the Yarra. Footscray and Brunswick East saw their populations grow by almost half. More typical was growth of 15 to 20 per cent in a decade in the populations of suburbs from Yarraville to Essendon, Preston, Fitzroy, Ivanhoe, Hawthorn and Caulfield.

(If Prosper Australia analyst Catherine Cashmore is right in estimating, from water records, that 82,000 homes in Melbourne, or almost one in 20, are permanently unoccupied, and they are overwhelmingly in inner and middle suburbs, urban consolidation might well have housed most of Melbourne's population growth were it not for absentee owners buying purely for speculation.)

The Bureau estimates refute claims that Melbourne's growth is concentrated in a few areas. Of 66 suburbs or groups of suburbs it identifies within 10 kilometres of the city, all but nine grew by at least 10 per cent in the decade – and 26 grew by at least 20 per cent. That trend has been under way for some time, and is now accelerating. Since 1991, the inner area of Melbourne has added about 300,000 people, increasing its population by 40 per cent.

That is a huge change, after decades in which its population had been slowly falling. Obviously more people means more congestion on the roads, and crowding on the trams and trains. But has it led to any wider reduction in the quality of life in those suburbs? That debate has yet to begin. It has added to demands for services, but also generated a wider variety of shops and restaurants, more choices. You don't hear of people quitting the inner suburbs in protest.

Just over half the growth in the past decade took place in suburbs more than 20 kilometres from the GPO. The Bureau's estimates show a growing proportion of it is in outer western and northern suburbs such as Point Cook, Craigieburn and South Morang, but with the south-eastern tail still wagging strongly in Cranbourne and Pakenham.

For homebuyers, that's where the affordable housing is, and they have no choice but to accept higher transport costs and travel times as the price of being able to own their own home.

As in the post-war migration years, the new settlers are moving in before the services. Cranbourne East station ought to be providing its new residents with a train service, but the state's self-imposed restrictions on new transport investment mean it won't happen for 20 years – unless, like the campaign to extend the South Morang line to Mernda in 2014, it becomes an election issue.

Sir Henry Bolte, Premier in those post-war years, was hemmed in by a huge backlog of infrastructure needs on one hand, and a recalcitrant Commonwealth closing off his financial options on the other. Forced to choose, Bolte chose to build schools, not transport infrastructure. His successor Dick Hamer set about making amends, building the underground rail loop and much else, but the Fraser government shut that down by halving his borrowing limit.

Then the Kennett government made us think government debt was a crime, and Victorian governments since have been afraid to build the infrastructure the city's booming growth requires.

The Andrews government has done better than its predecessors in this area. From very low levels, it has lifted its spending on Victoria's transport infrastructure, and improved its quality. But the state's transport investment is still modest, and the Abbott and Turnbull governments have sharply cut their contributions. Victoria has been allocated just 9 per cent of the Turnbull government's transport investment in 2016-17, whereas 39 per cent will be spent in the Prime Minister's home state of New South Wales.

Total investment in publicly-owned transport infrastructure in Victoria in 2016 was just $2.9 billion, whereas NSW, aided by Commonwealth largesse, spent $7.3 billion. Adding in privately-owned toll roads changed the numbers only slightly: $4.6 billion in Victoria, $8.9 billion in NSW.

For the five years to 2020, the Commonwealth has allocated $31 billion for transport investment, of which just $3 billion or 10 per cent will be spent in Victoria, as against $9 billion in Queensland and $10.5 billion in NSW. When 37 per cent of Australia's population growth is happening in Victoria, the Commonwealth's bias is indefensible.

Reports out last week that the two governments are talking about building a rail link to Melbourne Airport suggest the Turnbull government realises that it has to do more. But so long as it keeps reaching into Labor's reject pile to suggest projects, we won't get far.

There are more urgent priorities than an airport rail link, and perhaps none more so than improving speeds, reliability and service levels on the Traralgon line, to make it more feasible for people in the Latrobe Valley towns to find work in Melbourne.

Rapid population growth is a mixed blessing. It adds to the richness and diversity of urban life, but also to its costs and frustrations. It increases pressure on housing prices, and hence affordability. And in the years when Victoria has dominated the nation's population growth, the Bureau estimates that its output per head, net of inflation, has grown less than any other state: just 0.8 per cent in the eight years to 2016. Average incomes have grown just 1.2 per cent in the same period.

There is room for legitimate debate about whether we have got the balance right. Has the federal government got it right in setting an immigration target of more than 200,000 permanent migrants a year, plus more than a million residents on temporary visas? Or should we scale back to give ourselves more breathing space on infrastructure, housing prices and employment opportunities for our own children?

Few people in the Melbourne of 1950 could have foreseen how European migration would change the city's way of life, and its identity. How will this new wave of migration change the way Melbourne works? And how will they change its sense of itself?