Andy Murray sat at a defensive distance from the desk in the interview room and spoke in such soft tones that it was hard to relate the man you were seeing with the one who had tried, a few minutes earlier, to launch balls out of the biggest stadium built in the name of the sport. He had played three compelling sets of grand-slam tennis in front of its hardest audience, yet was coming over all matter-of-fact.

It is an irksome tradition here that the victors on the main stadium courts are offered a handful of balls upon which they scrawl their signature, then thrash them skywards to the people behaving most dementedly - there is plenty of choice - in the stands. Upon the fourth-round success against Stanislas Wawrinka, of Switzerland, that transported the British No 1 farther into uncharted grand-slam waters, Murray attempted to reach the top rows, where he had first watched tennis in New York as a fascinated 16-year-old in 2003.

It goes to the heart of the Murray of 2008, the grown-up champion-in-waiting who is as self-effacing as he is self-confident, that he announces he has worked out that he is probably going to be the next No 4 player in the world as if he is reading the weekend church notices. Others can eulogise, it is not his style.

Murray said before this US Open that all he could do was to place himself in a position to try to win a grand-slam tournament and see how it went from there. With his 6-1, 6-3, 6-3 destruction of Wawrinka, the world No 10, on the Arthur Ashe Stadium court, he has climbed four of the seven rungs and is nowhere near through testing his head for heights.

Murray’s play was implacably professional. Unlike his two previous rounds, he was in the groove from the first stroke, dismissing all Wawrinka’s best efforts with such disdain that, midway through the second set, the big screen was showing the USA network roving reporter’s chatter with celebrities in the stands because the tennis had lost its competitive fascination.

That will not be the case against Juan MartÍn Del Potro, of Argentina, today. When Nike, the clothing company, chose to spice up this event and bring Don King, the famed boxing promoter, along to front “The Grapple in the Apple”, it did not have Del Potro, one of its clients, or Murray (Fred Perry’s finest) in mind.

But the fallout from a spat in Rome in May - when Murray accused Del Potro of a verbal insult against Judy, his mother, who was watching in the stands - offers a spicy backdrop, to the extent that bookmakers are offering odds of 50-1 that the two will come to blows. Tennis-wise, the 6ft 6in right-hander is in the form of his life with a 23-match, four-tournament winning streak that includes victories over Andy Roddick, Richard Gasquet, Mardy Fish and Tommy Haas. That has launched Del Potro, who turns 20 in three weeks, into the top 20 in the rankings for the first time. “I’ve known him since we were really young and the fact we haven’t talked since May doesn’t bother me,” Murray said. “I wasn’t great friends with him before. I don’t need to be friends with him now.”

There is a bit of the Murray strut in Marcus Willis, the top-ranked British junior who will be 18 next month. He beat Dane Propoggia, of Australia, for the loss of two games yesterday to reach the second round of the boys’ singles.

Gilles Muller, of Luxembourg, who was slogging his way through ATP challenger events in Istanbul and Segovia in the preceding fortnight, reached the quarter-finals of a grand-slam tournament for the first time last night, defeating Nikolay Davydenko, the world No 5 from Russia, 6-4, 4-6, 6-3, 7-6. Muller was ranked No 130 two weeks ago, which meant he had to qualify here. With the result, Murray is guaranteed that world No 4 spot unless Roddick or Fernando González, of Chile, wins the title.

Novak Djokovic’s performance in defeating Tommy Robredo to reach the last eight was a perfect summation of his character. On the hottest day so far, the world No 3 from Serbia withstood the best that the Spaniard could throw at him to secure a 4-6, 6-2, 6-3, 5-7, 6-3 victory, at the end of which he thumped his heart, his thighs and tapped his forehand. It was a win that required him to call upon all of his virtues in abundance.