Last year, Acer’s market share grew by 3 percentage points, to 10.9 percent, while Dell gained just 0.1 percentage point, to 15 percent, according to the research company IDC. Acer has continued to narrow that gap this year, claiming 11.6 percent of the market to Dell’s 13.6 percent through the first quarter.

Mr. Lanci says he thinks that Acer can keep growing, especially in the United States and China  the two most prized regions for PC sellers. In addition, he’s steering Acer into cellphones, arguing that the growing similarities between smartphones and laptops play directly to Acer’s strengths.

“I think we have the know-how, and these two worlds are going to merge,” he says.

In the meantime, Acer has snatched the mantle of quick-moving, lean operator from Dell. Be it wireless technology or super-thin laptops with a long battery life, Acer often ships computers with new features before any other large PC maker. And when it spots a hot trend started by another company  netbooks, for instance, were the brainchild of Asustek, a fellow Taiwanese company  Acer follows in force, bombarding the market with low-cost products.

Paul S. Otellini, the chief executive of Intel, credits Acer with embracing its underdog role and taking big risks to disrupt the status quo. “They have done a spectacular job,” he says.

Acer’s quest comes with challenges, of course. Its low-cost operating structure leaves only so much money for research and development. H.P. knocks Acer as having a limited breadth of products and a dearth of the homegrown features that can command higher prices. And Dell has moved into retail, Acer’s home turf, while also releasing a flood of eye-catching new designs meant to tempt consumers.

“I think Acer is just one more competitor that doesn’t focus on anything other than public relations to win in the marketplace,” said Todd Bradley, the head of H.P.’s computer business.

Image Acer has risen swiftly on the strength of netbooks and laptops, and its chief, Gianfranco Lanci, sees an opening with smartphones. Credit... Ashley Pon for The New York Times

Such comments, however, come as H.P.’s revenue from the PC business has declined 19 percent in each of the last two quarters. Dell’s decline has been even more severe, with desktop sales falling about 30 percent each quarter. Acer’s overall revenue has fallen as well, but only 7 percent and 8 percent, respectively.