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The PC's fall from popularity helped drive a hard-hit Dell to take itself private, but the computer maker now sees some signs its business there is turning around. "We're seeing that a lot of the smaller players are leaving, which is giving us a bigger opportunity to go after that market," said Peter Marrs, vice-president of enterprise solutions for Asia-Pacific Japan at Dell. "The market has been declining here in Asia, but we continue to grow faster than the market." Read More PC shipments plunge, but Apple surges

Japan's Sony, India's HCL Infosystems and South Korea's Samsung and LG are among the players leaving the PC business or at least scaling back, he noted. Sony sold its PC business, VAIO, to investment fund Japan Industrial Partners in 2014, while HCL said in 2013 it would gradually phase out PC manufacturing. Samsung stopped sales of laptops in Europe last year, while LG said early in 2014 it would leave the "traditional PC market."

In 2013, Dell Chairman and CEO Michael Dell secured shareholder approval for his $25 billion offer to buy and take the firm private after a drawn-out battle. The company was once at the top of the PC business, boosted by its pioneering model of allowing customers to order custom-configured PCs online, while working closely with suppliers to keep costs low. But the company, which was getting most of its revenue from the PC business, ran into sharp headwinds as PC prices fell and its customers' tastes shifted toward tablets and smartphones. Read More Here's why Lenovo is sticking with PCs

Dell has around 14 percent of global PC market share, ranking third globally in the second quarter of 2015, after HP and Lenovo, according to data from Gartner. But globally, PC sales are still falling, with only around 251 million desktop and laptop units, or around $151 billion worth, expected to be sold this year, down from around 343 million, or around $218 billion, in 2012, Gartner said. Around 31.9 million units, or around $18.2 billion worth, are expected to be sold across emerging and mature Asia and greater China this year, the data show. The PC business in Asia so far appears to be avoiding one of the pitfalls seen in developed markets: companies encouraging using employees to use their own devices such as personal laptops and smartphones, rather than investing in capex. "Probably in other parts of the world, you see more of that, but I think here in Asia, we still see the normal deployment of company-owned assets and PCs," Marrs said. "Bringing your own device in, like a laptop, is a security and manageability concern."