* PMIs suggest euro zone decline deepening
* Economic rot taking root in Germany, France
* Worst of China growth slowdown may be over
* U.S. manufacturing improves, outlook still cloudy
NEW YORK/LONDON, Oct 24 (Reuters) - Euro zone businesses suffered another dismal month in October as factory output plunged in Germany, the area's top economy and exporter, while conditions improved slightly for U.S. and Chinese manufacturers.
Deteriorating conditions across Europe suggested the downturn in the 17-country euro zone would accelerate over the last three months of the year, according to Chris Williamson, chief economist at financial data firm Markit.
Markit's Composite Purchasing Managers' Index (PMI) for the euro zone, which polls around 5,000 businesses across the 17-nation bloc, fell to 45.8 this month, its lowest reading since June 2009. The index has now been below the 50 mark that separates growth from contraction since February.
Things were a bit brighter in North America and Asia.
A survey showed China, the world's second largest economy and a major exporter, was slowly recovering from its weakest period of growth in three years. While manufacturing contracted for a 12th straight month, output hit a three-year high and order books were their most robust since April.
The outlook was a bit more tempered in the United States . Its manufacturing sector managed to grow this month with Markit's manufacturing PMI index edging up to 51.3, bu t falling overseas demand and uncertainty surrounding U.S. elections and fiscal policy suggested the sector's recent struggles would continue in the months ahead.
``Europe is still struggling a lot and it's the United States' trading partner. There are some concerns about the fiscal cliff as well as the U.S. Presidential election,'' said Robert Van Batenburg, head of global research at Louis Capital Markets in New York. ``There is some measure of hope out there, but I'm skeptical about what will happen between now and March.''
That could keep pressure on the U.S. economy, which is expected to grow at a sluggish 2 percent rate this year.
Many U.S. companies have reported lower earnings for the quarter, hit by lack of demand and slower global growth.
Dow Chemical Co., the largest U.S. chemical maker, said it plans to cut 5 percent of its workforce and shutter 20 plants to counter slower global demand.
Corning Inc, the specialty glass maker, also announced planned job cuts to offset slower sales.
Worries about Europe intensified after a survey of manufacturing in Germany, the euro zone's biggest economy, in which the main index pl unged by more than expected to 45.7 from 47.4.
The rate of decline was even worse in France and illustrated that a slump that began with a debt crisis in Greece had spread to the euro zone's core economies.
``(It) reinforces concern that the economic downturn in the region may be deepening and widening,'' said Martin van Vliet, senior economist at ING.
In a separate report, Germany's Ifo institute showed business sentiment in the country dropped sharply to its lowest in more than 2-1/2 years, the sixth consecutive monthly fall.
``Any hopes of a rebound appear to have been dashed for now. Germany is heavily dependent on exports so a global slowdown is going to impact on Europe's growth motor,'' said Peter Dixon at Commerzbank.
The euro zone economy contracted 0.2 percent in the second quarter and is predicted to have shrunk 0.3 percent in the third, meeting the technical definition of recession.
Markit chief economist Chris Williamson said he expects an even greater contraction.
``We are more downbeat than the official data. The PMIs are running at levels in the third quarter and start of the fourth quarter historically consistent with GDP falling at about 0.6 percent,'' he said.
A recent Reuters poll predicted the euro zone economy may not recover until 2014.
Bad news has been flowing out of Europe's company boardrooms too.
Carmaker Volkswagen reported a fall in nine-month operating profit on Wednesday and sportswear maker Puma reported sales in the region dropped in the third quarter.
Heineken NV, the world's third-largest brewer, reported a stronger than expected increase in third-quarter revenue, but sold more beer everywhere except western Europe.
Markit's measure of services business expectations sank to its lowest reading since February 2009, at the nadir of the last recession and when world stock markets were tumbling.
STABILISATION IN CHINA
It was a different story for China, where the HSBC Flash Manufacturing PMI rose to a three-month high of 49.1 in October.
``(This) adds to recent signs of stabilisation of the Chinese economy, thus underpinning our view that the slowdown in activity is bottoming out,'' said Nikolaus Keis at UniCredit.
A Reuters poll taken after last week's GDP data showed economists anticipating a modest rebound in growth in the fourth quarter to 7.7 percent from the third-quarter's below-target 7.4 percent.
Even that figure would not be enough to lift full year expansion from an expected 13-year low, however.