December 20, 2004 10:07 AM EST

On the morning of Sept. 11, 2001, Adrian D. Smith, a well-known architect in the Chicago office of Skidmore Owings & Merrill, was in a meeting with Donald Trump Jr. The New York City developer was in Chicago to go over the design of a proposed Trump residential tower in that city that he had decided should be — what else? — the tallest building in the world, around 2,000 ft. In the midst of their meeting, the two men got word of the first plane that hit the World Trade Center. “When the second plane hit, we all rushed to the television to see what was happening,” says Smith. “That was the end of the meeting.” And also the end of the 2,000-ft. tower. A few weeks later, Trump’s people came back with a revised proposal — at 900 ft. or so.

The skyscraper was born in the U.S., and for most of the 20th century, it flourished here. Fifteen years ago, nine of the world’s 10 tallest buildings were in the U.S. (The 10th was in Toronto.) Now just two are: the Sears Tower in Chicago and the Empire State Building in Manhattan. All the rest are in Asia. A combination of factors — a sluggish commercial real estate market, skepticism about the profitability of very tall buildings even in good times, the rise of urban thinking critical of skyscrapers and the psychological fallout from 9/11—has discouraged today’s American developers from going very, very high.

More subtly, for some time before 9/11, the tall building had been losing ground as a symbol of power, wealth and importance, at least in Western countries, where museums, shops and restaurants became more significant status indicators. But elsewhere in the world, extreme verticals are still entirely in fashion, especially for developing nations looking to announce themselves. Just this year there was a new claimant to the title of world’s tallest building, the 1,670-ft. Taipei 101–named for the number of its floors. After it was completed, Chinese authorities and the developer, who were determined not to let their least favorite neighbor get ahead in the vertical space race, not only green-lighted a much delayed project, the Shanghai World Financial Center, but insisted on additional stories so that the building will have more occupiable floors than the tower in Taiwan.

The Pacific Rim is not the only place where the new “supertalls” are going up. Coming soon is the Burj Dubai, in Dubai, one of the United Arab Emirates. It was designed by the same Adrian Smith who did Trump’s tower. In 2008, when the Dubai building is complete, he says, it will rise to a height “of well over 2,000 ft.” He won’t say just how high. His clients don’t want to tip their hand to other builders who have projects in the planning stages. If the others knew where the bar was set, they could easily pump their towers up a few feet higher — or more than a few feet. Architects and engineers agree that it’s only a matter of time before a tower rises somewhere in Asia or the Middle East to 3,000 ft.–more than twice the height of either tower of the World Trade Center.

The right architectural language for those beanstalks is still up in the air. In many places Asia has become the last outpost of Postmodernism, the ornamental style that American architects tried for a while in the 1980s, struggling to link the office tower to older traditions of Western building by tarting it up with Gothic spires and classical pediments. Postmodernism was an awkward undertaking, and it fell out of fashion when architects began finding more interesting ways beyond the stylistic endgame of Modernism.

Not in Asia, however. Many Asian clients saw the plain glass-and-steel Modernist box as a Western import, remote from their national traditions. They wanted silhouettes that would recollect local styles. So the Petronas Towers in Malaysia, until recently the tallest buildings in the world, evoke the minarets of a mosque expanded to sky-high proportions. The Jin Mao Tower in Shanghai, by Skidmore Owings & Merrill, is a highly elongated pagoda. So is Taipei 101, a giant knickknack of a building that pushes the Postmodern idea to the edge of kitsch. Make that past the edge.

But more agreeable gestures are out there. Cesar Pelli, who designed the Petronas Towers, is also the architect behind Two International Finance Center in Hong Kong, a 1,362-ft. office tower executed in the Art Deco– flavored projectile form he has developed lately. And when it’s completed, the Shanghai World Financial Center, by the American firm Kohn Pedersen Fox Associates, will be one of the most elegant buildings in the world, a chisel-shaped tower with a giant oculus cut into its tapering top. It could prove that architecture, and not just construction, is headed to new heights.

Correction: The original version of this story incorrectly named the individual who met with Adrian D. Smith in Chicago on Sept. 11, 2001. It was Donald Trump Jr.

This story originally appeared in the Dec. 27, 2004, issue of TIME.

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