* Euro pinned at $1.3600 awaiting outcome of ECB meeting
* ECB seen cutting all its rates, but much already priced in
* Nikkei builds on rally, eyes April peak
By Wayne Cole
SYDNEY, June 5 (Reuters) - Asian share markets mostly tracked sideways on Thursday while the euro flatlined at $1.3600, all hostage to great expectations the European Central Bank will finally end months of dithering by easing policy further.
Japan's Nikkei was again one of the few movers rising 0.3 percent to 15,117 as bulls tried to extend a two-week rally to test the April top of 15,164.
Elsewhere, caution reigned with MSCI's broadest index of Asia-Pacific shares outside Japan all but flat.
South Korean shares dipped 0.25 percent while Australia's main index was off 0.3 percent
The only major data in Asian time is HSBC's measure of the China services sector for May which could show some pick up from April's reading of 51.4.
Wall Street was equally hesitant with the Dow ending up 0.09 percent, while the S&P 500 gained 0.19 percent and the Nasdaq 0.41 percent.
The economic outlook was no clearer after a mixed bag of U.S. data that included disappointing results on the trade deficit and private employment, but better news on the service sector.
Still, it was notable that JPMorgan's measure of global industry output boasted a strong rise of 1.5 points in May, hinting at a broadening and strengthening in world growth.
In currency markets, the euro held a tight orbit around $1.3600 awaiting the outcome of the ECB policy meeting at 1145 GMT and President Mario Draghi's news conference at 1230 GMT.
Economists in a Reuters poll expected the ECB to cut its main refinancing rate by 15 basis points to 0.10 percent and the deposit rate to -0.10 percent from zero.
Imposing a negative deposit effectively charges banks for parking their excess money at the central bank -- a step that may, or may not, encourage them to lend the money instead.
The ECB is also thought likely to launch a refinancing operation aimed at funding smaller business across the EU, but to stop far short of the sort of quantitative easing embraced by the U.S., UK and Japan.
However, with so much already priced in to markets it could be difficult for policy makers to proffer a positive surprise.
"We continue to think that risks going into ECB are biased to the central bank underwhelming the market and are tactically positioned for a bounce in EUR/USD," cautioned JPMorgan strategist Niall O'Connor.
"The ECB's tone and message will be just as if not more important than the alphabet soup of policy announced -- does this represent a step change or a sea change for the ECB?" he added. "We believe attitudes will change only gradually but we'll have to wait and see."
Yet, expectations of ECB action have helped drive German bond yields lower, giving the dollar a larger rate advantage. Indeed, U.S. two-year Treasuries are now offering a premium of 34 basis points over their German counterparts , the fattest margin in almost seven years.
A break below the recent trough at $1.3585 could see the euro gap to support in the $1.3475/$1.3500 area. The U.S. dollar index was steady at 80.639, while the currency kept most of its recent gains on the yen at 102.63.
Benchmark 10-year Treasury yields were at 2.595 percent after rising to levels not seen since mid-May.
In commodity markets, copper suffered its biggest one-day fall since mid- April amid jitters about the impact on financing deals from a probe at a Chinese port.
Benchmark copper was down 1.21 percent at $6,784.85 a tonne after sliding as far as $6,760, its lowest since May 12.
Gold was subdued at $1,243/80 an ounce, still pinned near a recent four-month trough of $1,240.61.
Brent crude for July delivery was last down 75 cents at $108.07 a barrel. U.S. crude eased 41 cents to $102.23 per barrel. (Editing by Shri Navaratnam)