They first came to Miami to design big, splashy trophy buildings — the museums, the concert halls, the university buildings and, in an unlikely, nowhere-else-but-here evolution, the Beach parking garages that transformed unlovely infrastructure into showpieces.

Now a corps of star-caliber architects from around the globe has set upon another prosaic staple of Miami’s urban landscape. And the luxury condo may never be the same again.

What they bring to Miami’s drafting table ranges from the outlandish to the über-restrained.

On the one hand, there is an Alien-like, 62-story tower in downtown Miami by the firm of Iraqi-born, London-based Zaha Hadid, and towering twin twisters in Coconut Grove by Denmark’s Bjarke Ingels Group, which has also designed a massive rental project along Fort Lauderdale’s Riverwalk that will appear to have cracked in two.

On the other, there is a streamlined Miami Beach tower by the firm of Britain’s Lord Norman Foster that recalls the sleekest of luxury cruisers; a gently tapered, trapezoidal Sunny Isles tower by Swiss superstars Herzog & de Meuron, whose woggly balcony columns evoke the classic Beach hotels and condos of the ‘50s and ‘60s; as well as the glassy, minimalist elegance of two low-rises on Ocean Drive south of Fifth Street by Mexican Enrique Norten’s TEN Arquitectos and the expansion of the venerable Surf Club by the American firm Richard Meier & Partners.

Think units as big as a house, extra-high ceilings and expansive balconies and terraces, angled and cantilevered just so to provide shade from the sun and frame multimillion-dollar views, and lots and lots of clear, high-tech, heat-repelling glass — in short, all the ultra-spare extravagance that developers and architects say their sophisticated clientele expects in a Miami pied-a-terre.

To be sure, many Miami architects produce top-notch work, including homegrown powerhouse Arquitectonica, responsible for scores of buildings across the city and the globe. Renown architects like I.M. Pei, Philip Johnson and most recently, Frank Gehry, have done work in Miami in the past. So have TEN and Herzog & de Meuron, both of whom did Beach garages. The latter also designed the new Perez Art Museum Miami. But none have undertaken residential buildings.

The starchitecture condo arms race, not unique to Miami, has been driven by developers whose post-recession strategy is focused on massively deep-pocketed buyers, most from abroad, who are willing to pay once-inconceivable prices for the cachet and pleasure of taking up residence in an architectural masterwork. The price floor is $1.8 million for a unit at Herzog & de Mauron’s Jade Signature, rising to $50 million for the duplex penthouse at Foster’s Faena House.

“It’s sort of a circular thing where buyers are willing to pay extra, I wouldn’t say for a brand, but for a certain quality of design,” Norten says. “It’s very hard to say exactly what it is. The wow factor is a comfortable, solid and elegant environment.”

True, says Lipe Medeiros, who has a contract to buy a 4,700-square-foot apartment for $5.9 million in the Hadid-designed 1000 Museum building. “I adore Zaha Hadid and her designs. I fell in love with the design and the way the structure looks,” said Medeiros, a Brazilian-born photography collector who previously owned a fashion design firm. Medeiros, who has a boutique real estate team, has also recommended the building to a handful of high-end clients.

The appeal isn’t only about the designer pedigree. “When you have a top-of-the-line architect, you will have a different attention to detail. Zaha will not let her name be dirtied by somebody else going in and cutting corners.… It’s going to be her postcard in Miami.”

Norten and architects from the other star firms say they have strived to design uniquely South Florida buildings, reconceptualizing old Miami eco-friendly techniques for positioning buildings and balconies to create shade and capitalize on breezes to encourage inside-outside living.

Some, including the Foster design for Argentinian developer Alan Faena’s ambitious plan for a new urban district along a dormant stretch of Collins Avenue, are eschewing the typical Miami tower-on-a-pedestal model. Faena will build underground parking so the building’s entrances will sit at ground and beach level amid lush subtropical gardens. So will Herzog & de Meuron’s Jade Signature.

“We have worked with some brilliant architects. But at Herzog they have an army of people who all contribute ideas and think about every detail of the project,” said Defortuna, who flew to Switzerland to audition the firm before hiring them. “If a solution they came up didn’t work with the budget, they came back with three or four alternatives that work for them and for us. They never give up.”