Serena seeks to cap comeback year with Grand Slam No. 24

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Family ties: Serena Williams hugs sister Venus after they met in the quarter-finals of the US Open in 2015

Serena Williams, riding an emotional rollercoaster as she adapts to juggling tennis and motherhood, seeks to end 2018 on a high with a record-equalling 24th Grand Slam title at the US Open.

The US great counts six US Open victories among her 23 Slams and with one more would match Australian Margaret Court's record for most major singles titles.

She could also join Court, Evonne Goolagong and Kim Clijsters as the only mothers to win Grand Slam singles titles, but since an impressive run to the Wimbledon final -- where she fell to Angelique Kerber -- Williams has endured a lackluster buildup to the hardcourt showpiece in Flushing Meadows.

"I'm still at the very beginning, this is a long comeback," she defiantly told reporters after a second-round loss to Petra Kvitova -- winner of five titles this year -- in the second round at Cincinnati.

"I just began, I just started," Williams said. "I'm definitely at the very, very beginning."

She had shrugged off an even bigger disappointment two weeks earlier -- a 6-1, 6-0 loss to Johanna Konta in San Jose that was the most lopsided defeat of her career.

Williams later revealed she had learned shortly before that match that the man convicted of killing her sister Yetunde Price in 2003 had been released on parole, something she "couldn't shake out of her mind".

It was another instance of personal matters intruding on the tennis court in a way they never have before, with Williams opening up about her struggles with post-partum emotions since the birth of daughter Olympia last September, and wrestled with feelings of inadequacy that many new mothers experience.

"I have been through a lot of stuff in my life, but I have never been through this," Williams said. "Having a baby and feeling with the emotions and the ups and downs and the fears and the excitement."

And then there's her game, worryingly inconsistent in six tournaments so far this year -- including the French Open where she withdrew before the fourth round with a pectoral injury.

"Basically, my whole game needs to improve," she admits, if she is to avoid her first season since 2011 without a Grand Slam singles title.

- Halep in form -

World number one Simona Halep arrives at Flushing Meadows buoyed not only by her first Grand Slam title at Roland Garros but by an impressive hardcourt campaign that included a victory in Montreal followed by a runner-up finish in Cincinnati.

The Romanian has reached six finals this year, displaying a new maturity on the court.

"Now she's understanding what the problems are, when she gets a little bit emotional how many points in a row she's losing because of that," Halep's coach Darren Cahill said.

"She's starting to see the structure and the momentum changes and the swings much better than she used to. That's why now she's able to turn matches around, where as once upon a time they used to slip away pretty quickly."

World number two Caroline Wozniacki arrives in New York amid injury uncertainty, having withdrawn from Washington with a right leg injury and then retired with a left knee injury from her second-round match in Cincy -- where she also played with a shoulder strapped.

Sloane Stephens, the world number three, will be in unfamiliar territory as she defends her first major title, but a third final in the last five Grand Slams appears to be within her reach.

Kerber will be aiming to expunge the memory of a first-round exit last year.

The Wimbledon champion has reached at least the quarters of each Slam this year and looks again like the player who won two majors in 2016 -- including the US Open.