Want to know why Apple is suing Samsung over Android, or why Microsoft is re-imagining Windows as a touch-friendly mobile OS? Look no further than Gartner’s latest report on European and worldwide sales in the third quarter of 2011.

First, this release shows PC sales in Western Europe, not helped by HP’s dithering over what to do with its PC division. Total shipments declined by 11.4%. Apple increased its unit share by 19.6% to 7.6%, which would be greater when measured by value since its computers command the highest prices, but still small relative to the entire desktop and notebook market. Netbook sales declined by 40%, presumably because people are buying Apple iPads instead. “Media tablets” including the iPad are not included in these figures.

Next, take a look at worldwide sales of mobile devices. Units are up 5.6% year on year, to over 4.4m devices in the latest quarter.

Then at the operating system breakdown for smartphones (115m devices). The operating system in features phones does not much matter. Android grabbed an amazing 52% of sales (from 25% a year earlier), versus Apple’s 15%. Gartner thinks Apple’s decline is a blip cause by customers waiting for iPhone 4S, but this is still an extraordinary result for Android. Symbian is down from 36.3% to 16.9% (the “burning platform”); RIM is down from 15.4% to 11%; Microsoft is down from 2.7% to 1.5% – is that burning any less?

It would be remarkable if Microsoft’ share does not increase at least a little in the fourth quarter, with the launch of Nokia’s Lumia and much more promotional activity, but on these figures it needs a miracle.