Laura Robson may have come off second-best to American Sloane Stephens in the first instalment in what could become a real Grand Slam rivalry here yesterday, but as the British teenager leaves Melbourne, she will do so with renewed belief that soon she may be competing for these titles.

If that seems a bit outlandish given her 7-5, 6-3 defeat came in the third round of the Australian Open, it is worth remembering that this time last year she was well beaten at the first hurdle by Jelena Jankovic and was ranked down at No 134.

After beating eighth seed and former Wimbledon champion Petra Kvitova to reach the third round, Robson's ranking is projected to be just outside the top 40. Having built on her run to the fourth round of the US Open last September, a couple of good weeks here and there in the next few months and she will be seeded for the French Open.

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The one spanner in the works could be a shoulder problem which happened after practice the day before her match with Stephens, hampering her serving in particular. Robson's serve is increasingly a big weapon in her game, but she did not deliver a single ace and her service speed was well down on her usual level.

"We still don't know what it is because I haven't had time to see the doctor or anything yet," a disappointed Robson said yesterday. "But these things happen and you just have to play through the pain sometimes."

Robson turns 19 tomorrow and there is no-one younger ranked above her. Stephens, who is not 20 until March, is her contemporary and friend and on the basis of progress made in the past 12 months, the chances are they will be facing each other many more times in the future. They entered this tournament on the back of a pairing in the Hobart Internatiional where the American defeated Robson in straight sets in the first round.

Here, with her serving handicapped, Robson could not win many free points and made plenty of unforced errors as she tried to take the attack to Stephens, but she produced enough evidence to suggest it might not be too long before the aggressor comes out on top against the counter-puncher.

"I would say I still need to work on shot selection in the points," Robson said. "Sometimes I still go for a bit too much where I'd be better off playing an easier shot rather than going for winners the whole time. I think I can improve on everything. Movement is still an in-progress thing. Lots of things, really."

Stephens, who will crack the top 20 regardless of how she does tomorrow against Bojana Jovanovski of Serbia, was hugely complimentary about Robson when discussing their potential rivalry afterwards.

"When I saw we were on show court two, the fourth-biggest court, I was like, 'wow, really, we're on this court?'," Stephens said. "It feels like we are turning into a Federer/Nadal rivalry."

There was a smile as Stephens said it, but if they both continue to progress, she may not be far off the mark. The American moves as well as anyone in the women's game, is hugely consistent and fights for her life every time she plays. That's why Serena Williams believes she may be her heir apparent at the top of the sport.

Robson, meanwhile, has been tipped for greatness ever since 2008 when, as a 14-year-old, she won the junior Wimbledon title. Injuries and growing pains slowed her progress but, as she turns 19, she is improving fast.

"Last year I lost here 6-2, 6-0 in the first round," she said. "It's a massive improvement. There are still so many things that can be worked on, but I toughed out two good wins. So it was a pretty good tournament."

If Stephens is the next Serena Williams, the current one continues to cut a swathe through the draw, her latest victim Japan's Ayumi Morita, who led 3-0 in the second set before Williams won six straight games to go through 6-1, 6-3. The five-times champion, chasing her third straight Grand Slam singles title and her 16th in all, next takes on 14th seed Maria Kirilenko for a place in the last eight.

"Maria has been playing consistent tennis, especially the past 16, 18 months," third seed Williams said. "She's been so consistent, so my goal is just to be really focused against such a player that's doing so well."

Williams turned her right ankle in the first round and has had it heavily taped in her matches since. Practice has not been overly rigorous but she maintains it will not affect her bid for the title. She said. "Today was a good match for me. I was involved in a lot of longer points, something I definitely wanted. I hope I can keep this level up and go higher."

Defending champion Victoria Azarenka survived her first battle of the tournament as she was pushed to a third set by American Jamie Hampton. It might have been even tougher, but Hampton was struggling with a back injury as the match wore on and eventually top seed Azarenka claimed a 6-4, 4-6, 6-2 victory.

Hampton later revealed she had two herniated discs in her back, diagnosed at the French Open last summer, but Azarenka barely noticed any change in her ability to cover the court.

"I didn't really feel she was hurt much," the Belarussian said. "It was a bit obvious when she was walking, but when the ball was in play she was going for her shots and they were on the line. It's always good to battle through not playing well. Towards the end things were going better for me, but she played an outstanding match."

Former world No 1 Caroline Wozniacki reached the last 16 with victory over Ukrainian qualifier Lesia Tsurenko, but the run of 42-year-old Kimiko Date Krumm was ended by Jovanovski as the Japanese, a semi-finalist in 1994, went down 6-2, 7-6.