You've seen them posing in magazines, performing in lecture theatres and maybe even shouting across the office. But it is unlikely you've ever sat behind a boardroom table and given Richard Rogers, Zaha Hadid, Rem Koolhaas or Norman Foster a grilling.

Well, now you can see what it might be like. The series of videos below offers a fascinating insight into how this generation of "starchitects" behaves under pressure, as they each pitch to win one of the most high-profile competitions in recent years: a new tower for L&L Holding Company on Park Avenue in New York. The site has such daunting neighbours as Mies van der Rohe's Seagram building, and it will be the first full-block office tower to be built on the street in almost half a century.

Proposals by Zaha Hadid, OMA, RSH+P and Foster + Partners. Photograph: John Hill/Archidose

Norman Foster won the contest last month with perhaps the most classic of the four designs: a sober stack of three glass blocks, separated with landscaped terraces and all tied together with linear ribbons of exposed steel. But watching the presentations, you wonder quite how much it came down to the design, over the fact that Foster seems to be the only one capable of articulating his idea with any clarity and confidence.

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Ever the gourmand, Richard Rogers talks briefly about his lunch, before handing over to softly spoken partner Graham Stirk, who proceeds to deliver a measured sermon on their proposal in the manner of a primary school teacher giving an assembly to year three. "We're quite interested in the term 'legibility'," he says hesitantly, before reassuring the board that "we're desperate to try and make it feel like one building that isn't sat on a funny suitcase".

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Choosing to present sitting down, Zaha Hadid begins by flattering the panel, saying: "Of course we are very excited to be here," at which her partner Patrik Schumacher audibly sniggers, before interrupting Hadid to take over the presentation. He talks of their design as embodying a "businesslikeness, robustness, restrained elegance", but falls down by appearing not to know the height of his own atrium.

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Showing who's boss, Rem Koolhaas delivers the entirety of OMA's presentation himself, but dwells exclusively on the building's external appearance and why it takes on a twisted form. "The site is pulled in two directions," he explains, "so we looked at shapes that express that double pull." He then shows the resulting corkscrew form from many different angles, remarking on how it has "a surprising amount of silhouettes". Which is not that surprising really.

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Finally, Norman Foster eschews PowerPoint. Instead, he stands before an easel, jacket off, manhandling boards into place one at a time, showing he means business. He talks in practical, non-nonsense terms: "At the base of the building, you would like big footprints and tall space," describing specific spaces by their dimensions. He also knows how to talk the panel's language, declaring the design is the result of the corporate triumvirate of "design, market research and marketing". He also concludes by hammering a final nail in the coffin of his rivals: "To be distinguished and notable, this building doesn't have to indulge in a 'look at me' hysteria of sculptural shapes and so on."

In these high-profile invited competitions, organised by risk-averse boards of corporate bureaucrats, it is not hard to see why Foster so often triumphs. It is not only because he pedals a tried-and-tested brand, as a globally renowned safe pair of hands, but because he is one of the few principals of a practice this size with the ability to give the impression of having a personal grasp of every detail of the scheme. As a result, the client is wooed into feeling that they are paying for a building in which every feature has been drafted by hallowed hand of Norm himself – a spell that he casts by brandishing a felt-tip pen.