* China activity surveys hint at some levelling out, no rebound
* BOJ survey shows business sentiment improving, spending plans up
* South Korea and others still under a cloud
* More stimulus expected in second half to boost growth
By Ian Chua
SYDNEY, July 1 (Reuters) - Growth in China's services sector picked up in June while big Japanese companies planned to ramp up spending at the fastest pace in a decade, offering hope that prospects are improving for Asia's largest economies despite sluggish factory growth.
Wednesday's data fuelled expectations that the wobbly global economy may start levelling out in the second half of the year, but the outlook remains murky, with fears that Greece's debt crisis could splinter the euro zone and worries about whether China can avoid a stock market crash keeping investors on edge.
Activity in China's factory sector expanded slightly in June though not as much as expected, official surveys showed, suggesting the economy may be starting to slowly level out after a raft of support measures including interest rate cuts and more infrastructure spending.
Japanese factories barely expanded but a private report showed a strong pick-up in export orders, while a Bank of Japan survey showed a strong bounce in business confidence and spending plans, a welcome sign for premier Shinzo Abe's economic revival strategy which has seen limited success in nudging firms to boost wages and investment.
"When you have two of the biggest economies in the world showing positive readings, that is encouraging. They also come on the back of some good readings out of the United States," said Craig James, chief economist at CommSec in Sydney.
Yet reports from South Korea, Taiwan and Indonesia provided a more sobering read that still pointed to challenging conditions for many economies in the region.
The unending uncertainty over Greece also dampened confidence, though Asian markets held up well on Wednesday.
Similar activity surveys are due from Europe and the United States later in the day.
Though Greece makes up only about 2 percent of the euro zone economy, fears of contagion to other weak EU members could overshadow recent signs that businesses are in better shape.
In the U.S., the ISM factory PMI is expected to accelerate, reinforcing views the Federal Reserve could start raising interest rates in September, though a healthier U.S. economy is not giving as big a boost to Asia's exports as in the past.
H2 BOUNCE OR DEJU VU ALL OVER AGAIN?
To be sure, Asian exporters and global policymakers have made the same bad calls over and over again in past years, betting that advanced economies will recover strongly, but sustained turnarounds have repeatedly proved elusive.