A waiter holds a drinks tray in a make-shift hotel lobby during the official launch of InterContinental Hotels Group's (IHG) new hotel brand called Hualuxe Hotels and Resorts, held inside the Forbidden City in Beijing March 19, 2012. REUTERS/David Gray

By Ross Finley, Andy Bruce and Steven C. Johnson

LONDON/NEW YORK (Reuters) - Service industry growth slowed sharply in China as 2013 drew to a close but picked up across most of Europe, while U.S. firms hired more workers despite slower growth in activity last month.

The surveys released on Monday underscored a still uneven pace of global economic growth and suggested an onslaught of central bank stimulus is unlikely to dry up anytime soon.

Asian shares fell to a three-week low after the HSBC/Markit China services purchasing managers' index (PMI) fell to a two-year low of 50.9 from 52.5, highlighting anxiety about the world's second largest economy.

"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.

Indeed, most signs point to ongoing improved U.S. growth, and recent data has been robust enough to persuade the Federal Reserve to start winding down its monthly asset-purchase plan.

Even so, the economy is seen as not strong enough to withstand higher interest rates for a while, with the Fed not expected to raise them for at least another year, and Fed officials have stressed that unemployment remains uncomfortably high.

Business surveys from the Institute of Supply Management and Markit showed growth in the vast U.S. services sector slowed a bit in December.

But hiring was a silver lining in both reports, which showed employers took on more workers.

"The U.S. economy appears to have ended 2013 on a strong note, especially in relation to hiring," said Chris Williamson, Chief Economist at Markit, suggesting the upturn "sets the scene" for strong employment across industries in December.

The Markit survey for the euro zone went the opposite way, with the composite index 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.

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.

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.

DISINFLATION TAKES HOLD

Inflation pressures, which have been dormant in Western economies for many years now, have taken a back 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.

Consumer price inflation in Germany rose 1.4 percent in the year to December, data showed on Monday, while reports from other countries showed a slight acceleration.

The euro zone PMIs showed new orders 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.

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," said Commerzbank's Dixon.

U.S. inflation has also been tame, with the Fed's favoured measure of non-food, non-energy prices up 1.1 percent in the year to November.

Some worry that could change quickly if growth continues to pick up through 2014, a year that will still see the Fed injecting money into the economy, albeit at a slower pace.

Philadelphia Fed President Charles Plosser last week said he worried that inflation could rise quickly if banks start to release the $2.4 trillion in excess reserves they now hold.

(Writing by Ross Finley and Andy Bruce; Additional reporting by Steven C. Johnson and Ryan Vlastelica in New York and Xiaoyi Shao and Jonathan Standing in Beijing; Editing by Alison Williams and Chizu Nomiyama)