Acer has come from behind to knock Dell off its perch as the second-largest PC vendor in the world, and Dell is still hurting from its loss to HP which claimed Dell’s old No. 1 title three years ago.

Acer president Gianfranco Lanci (pictured) just predicted Tuesday that Acer would dethrone Dell’s shipments over the next two quarters. He also thinks he can “breach the gap with HP” in terms of notebooks, netbooks and smartphones.

Gartner and IDC read the taro cards again Wednesday and – after turning over the death card in Q1 and 2 when PC units dropped globally 6.8% and then 2.4% – found they were up a stronger-than-seasonal 2.3% in Q3 to 78.1 million units (IDC) or at least up 0.5% to 80.9 million (Gartner).

Doesn’t much matter, both estimates are above most people’s expectations and last year’s third quarter was very strong, a point of comparison that should be taken into account.

The last time IDC shuffled the pasteboards they said PC units would be down 2.9% in Q3. Gartner’s auspices said they’d be down 5.6%. They were both fooled by back-to-school sales and China.

As Intel indicated Tuesday, the consumer and notebook PCs saved the day; the enterprise is the weak sister, which explains Dell’s fall from grace. It depends on those businesses that are sitting on their pocketbooks.

ASPs were probably down double-digits again – maybe 20% or more, Gartner suspects; price cuts and cheapo netbooks probably pushed Acer ahead of Dell. Gartner figures netbooks for 20%-30% of the market, up from 17% in Q2. IDC says netbook sales next year should tally 30 million units.

Gartner worries about those ASPs, warning that “PC vendor performance cannot be determined solely by unit market share gains alone as related revenue and margin performance are key to surviving in a very competitive market.” It sees revenue losses despite the gains.

HP, which is stronger than Dell in retail sales, gained market share. Its shipments according to IDC were up 9.3%; it now owns 20.2% of the whole global market. Acer, which bought the consumer-oriented Gateway and Packard Bell but “outperformed the market in virtually all regions,” is second with 14%, its shipments up 25.6% to 10.96 million units.

Dell’s shipments were dropped 8.4% to 9.95 million units, giving it 12.7% of the world market.

Gartner figures US units were up 3.9% to 17.8 million units, while IDC thinks it was more like 2.5%.

Dell’s No. 1 position in America hasn’t collapsed completely yet, but HP is neck-and-neck, close enough that it’s hard to tell which is really ahead. IDC gives HP the lead by half a point. Gartner gives Dell the same edge. Acer is number three, with 61% growth.

Dell did okay in emerging markets. Japan as a geography is still off for everybody, down double-digits. EMEA also declined.

Lenovo came in fourth worldwide with 6.99 million units and Toshiba fifth with 4.04 million.

Apple’s shipments, which only count in the US, where it’s fourth, were up 11.8%, giving it 9.4% of the market.

The bottom fell out of the market in the fourth quarter of last year so when Gartner forecasts 29.6% growth this quarter, it’s a compare distortion. Gartner writes off any real impact on unit growth by the release of Windows 7 this month. Everybody’s anticipating a pretty massive hardware refresh next year.