LONDON, April 13 (Reuters) - Sovereign wealth fund (SWF) assets all but stalled at $6.59 trillion in the year to March 2017 due to a combination of weak markets, low oil prices and shifts in government policy, a report from research provider Preqin showed.

Total assets under management have levelled off in the last two years, with growth of just 3 percent in 2015 and 1 percent in 2016, when assets stood at $6.51 trillion.

This is in contrast to previous years, when SWF assets grew by 17 percent between December 2011 and December 2012, and by a further 16 percent the following year, Preqin said in a report received on Thursday.

"Macroeconomic headwinds, low oil prices, and shifts in domestic and economic policy from their governments have all contributed to this tapering off," Selina Sy, editor of the 2017 Preqin Sovereign Wealth Fund Review, said.

Some oil-backed funds have reined in spending as their governments have used them to close budget gaps. Oil prices LCOc1 are currently around $56 a barrel, a long way off the highs of $115 touched in June 2015.

In another sign of belt-tightening, SWFs pulled $37.8 billion from global stock and bond markets in 2016, according to separate data from research firm eVestment.

However, hydrocarbon-backed SWFs grew by $60 billion in the 12 months to March 2017, Preqin said, suggesting the worst of the selling may be over.

In fact, only 29 percent of SWFs suffered a decline in assets in the last 12 months, versus 36 percent in the previous year.

A slim majority of 51 percent saw their assets increase in the year to March 2017, with SWFs funded by non-hydrocarbon commodities growing by $10 billion, as did those funded by non-commodity sources.

The investor class remains dominated by a handful of heavyweights with the 10 largest funds collectively holding $5.2 trillion - 79 percent of the whole. They include Norway's $915 billion fund, the world's biggest, and the China Investment Corporation, with $800 billion under management.

At the other end of the scale, 45 percent of SWFs hold less than $10 billion.

The sector continues to evolve, with Abu Dhabi creating a $125 billion fund by merging Mubadala Development Company and International Petroleum Investment Company.

Some smaller SWFs, such as the Turkey Wealth Fund, have also launched.

The proportion of SWFs investing in alternatives has grown, with 61 percent allocating to private equity, a record high, and 63 percent to real estate.

Some 63 percent of SWFs were also invested in infrastructure, liked for its ability to deliver steady, visible cashflows over the long term.

(Reporting by Claire Milhench; Editing by Susan Fenton) ((claire.milhench@thomsonreuters.com; +44)(0)(207 542 3571; Reuters Messaging: claire.milhench.thomsonreuters.com@reuters.net))