* Williams looks for first Cincinnati title
* Li through to semi-finals (Adds late matches)
CINCINNATI, Aug 15 (Reuters) - As the tennis world took stock of Marion Bartoli's shock decision to retire, Victoria Azarenka tried to put the focus back on court with a controlled display against Magdalena Rybarikova at the Western and Southern Open on Thursday.
The world number two's 6-3 6-4 third round victory was impressive but it could not turn attention away from Bartoli, the Wimbledon champion having stunned the sport 24 hours earlier by announcing she was quitting following a second-round defeat.
Even when world number one Serena Williams closed out the action under the center court floodlights with a 63 minute 6-4 6-1 demolition of Germany's Mona Barthel, Bartoli's departure remained firmly in the spotlight at the sprawling Lindner Family tennis center.
"Marion Bartoli is such a great fighter and she has a great attitude," Williams told reporters. "I remember the first time I saw her, I was actually in Paris for the Paris Indoor Championships.
"It was a long, long, long time ago, probably in like the early 2000s, and I just remember her being so young and working so hard, and that was her whole career.
"It just shows you how much and how far you can go by working so hard. She's had a great career by winning Wimbledon as well. It doesn't get better than that."
Williams, however, could soon be back making headlines as she tries to fill one of the few holes in her glittering resume this weekend with a first Cincinnati crown.
In a career that has garnered 54 singles titles, including 16 grand slams, Williams has won just about everything there is to win in her sport but one of the WTA Tour's most prestigious tournaments remains absent from that long and impressive list.
After a sluggish performance against Canadian Eugenie Bouchard in her opening match, Williams was firing on all cylinders against an overmatched Barthel.
"I didn't know much about her, though, but I knew her name," said Williams, who will next face Romanian Simona Halep, who beat Bartoli in what was the final match of the Frenchwoman's career.
"She's an interesting player. She seemed so light and so smooth so you don't expect a ball to come that hard.
"That was a little surprising but once I got used to it, it was a little better."
There was nothing surprising about Azarenka's third round match as she moved easily into the quarter-finals, despite problems with her serve during an uneven match that featured 13 breaks.
"Today there was sometimes a little bit of trouble serving but overall I felt better than I did in my first match," Azarenka said. "I was much more controlling the game. It was really up to me today, I felt.
"I was doing everything I wanted to do but I still feel there can be a lot more improvement."
Li Na's Cincinnati title defence also picked up steam as the fifth-seeded Chinese rolled to a 6-4 6-4 win over ninth seed Angelique Kerber of Germany.
Before Thursday action was completed, Li found herself through to the semi-finals when Polish fourth seed Agnieszka Radwanska, who beat Elena Vesnina 6-0 6-2, withdrew from the tournament to attend her grandfather's funeral.
In other third round action, Italian doubles partners Sara Errani and Roberta Vinci went toe-to-toe for a spot in the final eight with the 12th seeded Vinci coming out on top, beating her sixth seeded compatriot 6-4 6-3.
American Sloane Stephens, second round conqueror of world number three Maria Sharapova, appeared on course for another upset after taking the opening set off 14th seeded Jelena Jankovic before the Serb rallied to claim a 3-6 7-5 7-5 win.
Tenth seed Caroline Wozniacki of Denmark advanced to the final eight with a gritty 3-6 6-2 6-3 win over Czech seventh seed Petra Kvitova while Halep continued her mastery of grand slam winners, edging Australia's 2011 U.S. Open champion Sam Stosur 6-4 4-6 6-2. (Editing by John O'Brien)