* Business surveys point to better, if patchy growth
* Euro zone firms end 2013 with faster expansion
* Chinese services growth slows in December
* Strong rate of expansion in Britain slips
By Ross Finley and Andy Bruce
LONDON, Jan 6 (Reuters) - Service industry growth slowed sharply in China as 2013 drew to a close but picked up across most of Europe, suggesting still very uneven global economic performance even as most signs point to a strengthening U.S. revival.
Taken together with business surveys on manufacturing published late last week, the data suggest that an onslaught of global central bank stimulus has had some impact but is not likely to halt any time soon.
Indeed, while business has picked up in many places, particularly in the euro zone which only recently escaped recession, inflation has been on a downward trend in most industrialised countries.
Asian shares fell to a three-week low after news the HSBC/Markit China services purchasing managers' index (PMI) fell to a two-year low of 50.9 from 52.5, underscoring nervousness about how the world's second largest economy is performing.
The equivalent Markit survey for the euro zone went the opposite way, rising to 52.1 from 51.7, with new orders coming in at their fastest pace in more than two years. Any number above 50 denotes expansion.
"That just goes to confirm everyone's suspicions that the Chinese economy is shifting down onto a lower growth path, and that we will see a more balanced growth pattern across the world this year," said Peter Dixon, economist at Commerzbank. He expects improved growth in Europe and the United States.
The U.S. ISM non-manufacturing survey, comparable with the euro zone and Chinese PMIs, is due at 1500 GMT and is expected to show faster growth there.
Markit said that while the euro zone data suggested only a 0.2 percent quarterly rate of economic growth, "the PMI signalled a strong turnaround in the health of the economy during the course of 2013".
The question is whether that can be sustained, particularly when demand in China, one of the euro zone's biggest trading partners, is just bumping along.
Inflation pressures, which have been dormant in Western economies for many years now, have taken a second seat to discussions about the world outlook but could again come to the forefront given current trends.
The European Central Bank, which targets inflation at just under 2 percent, cut interest rates in November to a record low of 0.25 percent after surprise news of a plunge in euro zone inflation to just 0.7 percent.
German inflation data due at 1300 GMT could set the tone for financial markets on their first major start to the year as many return from holidays.
The latest Reuters consensus is for inflation to tick up to 1.4 percent from 1.3 percent, but the lowest forecast in the sample is for a fall to 1.1 percent. Data from states earlier on Monday suggest a slight acceleration.
The euro zone PMIs showed new orders coming in at the fastest pace since June 2011, while the employment index hit the 50 mark for the first time in two years - meaning employers are now hiring as many staff as they are laying off.
While showing a fairly broad-based upturn across most of the euro zone's major economies, France remained a laggard.
"Certainly in the euro zone at least, momentum is just about holding up," said Commerzbank's Dixon.
"But there are indications that the economy is beginning to make some kind of progress, and places like Spain - which got clobbered during the downturn - seem to be showing quite a rapid rate of recovery."
Growth in Britain's services sector slowed unexpectedly in December, but confidence rose and the economy still looks likely to have recorded its strongest expansion since 2007 last year.
"More strong growth looks likely as we move into 2014," said Markit's chief economist Chris Williamson, on the prospects for the UK.