Lenovo is within a rounding error of becoming the world’s No. 1 PC company.

The firm that operates its executive headquarters in Morrisville and is built around IBM’s PC division which it acquired in 2006 is just two tenths of a percentage point behind HP in global PC market share, research firm Gartner says.

Lenovo continued its march toward more global market share in the second quarter as it surged to 14.7 percent, up two full points a year ago. HP’s fell two points. Overall industry growth was flat compared to a year ago, so Lenovo is gaining at it’s competitors’ loss.

But Lenovo, which continues to launch a wide variety of cutting-edge new products from laptops to desktops, isn’t satisfied with the growth. In an interview last week, David Schmoock, Lenovo’s senior North American executive, declared: “It’s not over.” 

Statistics from the other major firm that tracks the global PC market, IDC, shows Lenovo trailing HP by a razor-thin margin as well: 14.9 percent vs. 15.5 percent.

In the U.S., IDC reports that Lenovo has cracked the top 5 with a No. 4 ranking and 8 percent market share. “We have a way to go to be No. 1 in North America,” Schmoock noted. But that goal will be achieved, too, he said, “if we build this right.”

Lenovo recently expanded office space in Morrisville and capacity of its distribution center in the Triad in order to accommodate growth.

Chairman Yang Yuanqing and other executives have made clear over the past year that they want to topple HP from the top spot while at the same time growing business worldwide. Its sales grew 15 percent in the second quarter even as overall PC sales stagnated.

“Lenovo’ s shipment growth continued to exceed the worldwide average, significantly narrowing the market share gap with HP,” Gartner notes in its report.

“Lenovo has been very aggressive to expand through a series of acquisitions, as well as aggressive pricing,” it adds. “Lenovo’s aggressive expansion damaged its competitor’s performance, namely HP and Dell, by taking shares from them.

According to Gartner, Lenovo shipped 12.8 million PCs in the second quarter, just 200,000 behind HP. Acer toppled Dell from the No. 3 spot with 9.6 million units shipped to Dell’s 9.4 million. HP shipments declined some 1.8 million and Dell’s were down 1.1 million.

Both HP and Dell are putting less importance on their PC divisions, although under new CEO Meg Whitman HP scuttled plans to sell off its computer group.

Gartner did note one concern about Lenovo – inventory.

“Lenovo showed significant growth in [Europe, Middle East, Africa] though there is growing concern of the inventory build toward the second half of 2012,” Gartner said.

IDC measures PC data somewhat differently than Gartner but still showed strong year-over growth for Lenovo at 12.9 million machines, up from 10.2 million.

“Lenovo remained in second place, but narrowed the gap between itself and HP considerably,” IDC reported.

“While Lenovo continued to grow much faster than the market, it too experienced slower growth than in recent quarters.”