* US services sector expands in Dec, hiring up sharply
* U.S. employers add 155,000 jobs across economy in Dec
* Surveys suggest euro zone downturn is easing
* UK service sector declines, fourth quarter contraction seen
By Steven C. Johnson and Andy Bruce
NEW YORK/LONDON, Jan 4 (Reuters) - Activity in the dominant U.S. services sector perked up in the final month of 2012, while hopes grew that Europe may be through the worst of its economic slump, surveys showed on Friday.
Britain's vast services sector, however, contracted for the first time in two years, suggesting the broader economy probably shrank as well in the final three months of 2012.
Worldwide, private sector business growth hit a nine-month high, boosted largely by service-oriented firms.
But none of the data suggest growth is robust enough to pressure central banks on either side of the Atlantic to tinker with highly stimulative monetary policies.
The Institute for Supply Management said its index of U.S. service firms grew at its fastest clip in 10 months in December, boosted by a rise in new orders. The pace of hiring in the sector hit a five-month high.
Throughout the U.S. economy, employers added 155,000 new workers last month, a separate report on Friday showed. Gains were distributed broadly, from manufacturing and construction to health care, which economists say suggests the economy would probably grow by about 2.0 percent in 2013.
"The overall tone was one consistent with modest economic growth," said Joshua Shapiro, chief U.S. economist at MFR, a global consulting firm based in New York.
The 17-country euro zone, on the other hand, probably closed out the year in recession, though evidence that the pace of contraction in the service sector had slowed suggested things may be turning around.
"I think (the euro zone PMIs) are showing a decisive bottoming-out of activity," said James Nixon, chief European economist at Societe Generale. "Now, the actual levels of the surveys are still consistent with GDP declining, but at least things aren't getting worse any faster."
According to financial information firm Markit, the euro zone's composite PMI, which measures the activity of thousands of companies, rose to 47.2 last month, its highest since March.
The decline eased among firms such as banks and restaurants, which comprise the bulk of the euro zone economy, though things looked worse for manufacturers.
"The surveys at least bring some substance to the belief that the worst is over and that a return to growth is in sight for the region in 2013," said Chris Williamson, chief economist at Markit.
The UK services PMI, however, slipped to 48.9 from 50.2, sagging below the 50 mark that divides expansion and contraction for the first time in two years.
"The broader picture is that for some time the economy has been bouncing around the bottom ... and I think this is likely to stay with us for the next couple of quarters," said Rob Wood, chief UK economist at Berenberg Bank.
Survey compiler Markit said the figures suggest Britain's economy shrank 0.2 percent in the final quarter of 2012, a slightly bigger drop than most other private-sector forecasts.
HOPES PINNED ON CHINA, U.S.
Friday's European data followed news that China's services sector saw its slowest rate of expansion in nearly a year and a half in December, although the HSBC services PMI still pointed to a modest revival in economic growth.
Fears that China's economy would hit the skids kept investors on their heels in early 2012, but data in the second half of the year suggested the world's second biggest economy would avoid a hard landing and continue to grow modestly.
With Europe likely to remain in recession, the world economy will increasingly depend on China and the United States to provide the fuel for continued growth.
Recent U.S. data, particularly from the labor market, has been encouraging, not least because firms continued to hire in December despite a looming government budget crisis that many feared would bring recession in 2013 if not solved.
"This supports the view that the economy is picking up steam and employers added to payrolls even with worries about the fiscal cliff," said Andrew Wilkinson, chief economist strategist at Miller Tabak & Co in New York.
The U.S. Congress struck a deal to avoid going over the "fiscal cliff" of tax hikes and spending cuts on New Year's Day, though decisions on important spending issues were delayed.
Bond markets also got a scare on Thursday when published minutes from the Federal Reserve's last meeting revealed some officials thought it would be appropriate to wind down the central bank's open-ended asset purchase program, known as QE, before the end of 2013.
That propmted a spike in long-dated bond yields, though Friday's data showing the U.S. jobless rate rising to 7.8 percent eased some of those fears.
"When is comes to Fed policy, this report should keep it steady," said Tom Porcelli, chief U.S. economist at RBC Capital Markets. "There was talk of a scaling back of QE yesterday, but this number is a snapshot and is basically where it was when the Fed decided to do more QE last month."
Economists think the European Central Bank may go further and cut interest rates again.
Euro zone policymakers discussed but decided agianst cutting rates from a record low 0.75 percent at last month's meeting.