By Jonathan Cable

LONDON, Sept 3 (Reuters) - Global service sector surveyshighlighted a growing divergence in economic recovery on Fridaywith a pick up in growth in China and Germany but slowdowns inBritain and Spain and an expected deceleration in the UnitedStates.

The data follows sister surveys which earlier this weekpainted a similar picture for the manufacturing sector althoughsigns of expansion in China and the U.S. revived some investorconfidence.

China's service sector expanded at its fastest pace in fourmonths in August on the back of strong domestic demand but theheadline figure was below the long-run average of the series.

HSBC said its Purchasing Managers' Index for Chineseservices, which account for much less of output than in moredeveloped countries, rose to 57.6 in August from 56.3 in July.

The pace of recovery in the 16-nation euro zone, whoseeconomy is heavily weighted to the service sector, was barelychanged in August from July but signalled a growing split, witha pick up in Germany offset by Spain sliding back intocontractionary territory.

Markit's Eurozone Services Purchasing Managers' Index forthe service sector, which accounts for roughly two-thirds of theeuro zone economy, nudged up to 55.9 in August from 55.8 in July-- a strong overall reading.

"The surveys highlight the uneven performance of the eurozone economies, with Germany currently performing very well,France decently, Italy growing modestly and Spain and Irelandstill struggling to develop recovery," said Howard Archer, chiefEuropean economist at IHS Global Insight.

The bloc's economy expanded 1.0 in the second quarter overthe first, its fastest pace in more than three years, althoughthat was really a reflection of German resurgence.

Spain's services PMI fell to 49.2, the first time the indexhas slipped below the 50.0 line that separates growth fromcontraction since February.

And Britain saw its dominant service sector activity growlast month at its slowest pace since April 2009, with a markedfall in hiring as employers worried about an economic slowdownand public spending cuts.

The headline Markit/CIPS services purchasing managers' indexdropped to 51.3 in August from July's 53.1, a much sharper fallthan the decline to 52.9 forecast in a Reuters poll.

Governments are turning their focus to slashing budgets asthey face up to paying off the billions of dollars pumped intoeconomies to drag them out of the worst post-war recession.

PAYROLLS FORECAST TO FALL AGAIN

A similar index for the United States, due later on Friday,is expected to show a slowing growth rate for services in theworld's biggest economy but all eyes will be on U.S. jobsnumbers at 1230 GMT.

A reluctance by firms to add staff amid the economicuncertainty and relentless layoffs at cash-strapped state andlocal governments is expected to produce a third straight monthof decline in non-farm payrolls.

"In the euro zone there is not at the moment the risk of adouble dip, a risk that instead is present in the UnitedStates," Hans-Werner Sinn, president of Germany's IFO economicresearch institute, told reporters in Cernobbio, Italy.

U.S. growth braked to a 1.6 percent annualized rate in thesecond quarter after a brisk 3.7 percent in Q1.

With unemployment stuck near 10 percent and the impact ofthe government's $862 billion economic stimulus fading,investors worry that even if the U.S. economy avoids adouble-dip recession it may face a period of near-stagnation.

The big question is whether Asia and Europe's biggest powerscould carry on prospering or would inevitably be dragged down bythe world's largest economy, whose markets they are stillheavily reliant on for export demand. (Additional reporting by David Milliken and Andy Bruce inLondon, Alan Wheatley in Beijing and Nigel Tutt in Milan, ,editing by Mike Peacock)