* Fund value equates to $190,000 for every Norwegian
* Main challenge is reigning in public spending from fund
* Should fund management be separated from central bank
* Should fund go into unlisted shares, infrastructure
* Next opportunity to make changes will be Spring 2018 (Adds detail)
OSLO, Sept 12 (Reuters) - Norway's sovereign wealth fund, the world's largest, totalled $1 trillion for the first time on Tuesday as booming global stock markets and a rising euro lifted the value of its assets.
Oslo has grown increasingly dependent on the fund for public spending and its record value comes a day after Erna Solberg won an historic second term as Norway's prime minister.
Solberg's new government will now oversee a planned overhaul of the fund, in particular of its governance and strategy, which is expected in the coming months.
"There is an ongoing process towards a modernisation of the mandate of Norges Bank. This process was initiated by the Solberg I government and the (election) outcome should help hasten this process," Danske Bank said in a note to clients.
Established in 1998 to save oil and gas revenues for future generations, the fund is now worth about 2.5 times Norway's annual gross domestic product, against original projections it would peak at 1.3 times GDP in the 2020s.
A live update on the fund's website showed its value at 7.851 trillion Norwegian crowns at 1034 GMT, corresponding to $1 trillion according to Thomson Reuters Eikon currency data, or $190,000 for every man, woman and child in Norway.
But despite the growth in the fund's size, its use for public spending has rung alarm bells, with the central bank governor warning in February that it could make Norway too reliant on an uncertain source of income.
"Regardless of which government we get, the challenge will be to use less oil money," Erik Bruce, chief analyst at Nordea Markets, said.
Under a recently revised rule, governments can spend 3 percent of the fund's value per year, down from 4 percent, corresponding to 235 billion crowns of the current size. The 2017 budget has earmarked 221 billion crowns for spending.
Two issues are up for review, the first being whether the fund's management be completely separated from the central bank.
The second is whether the fund should be allowed to invest in new asset classes, including unlisted shares and unlisted infrastructure projects, to boost its rate of return, something that is supported by the fund's existing managers.
"The bank's explicit position is that we will get a higher return and a lower risk by investing in infrastructure," CEO Yngve Slyngstad told Reuters in June.
Investing in airports, roads, bridges or wind farms -- has been a hot topic in recent months, but the finance minister, Siv Jensen of the populist Progress Party, has twice declined to bring the proposal to parliament, citing political risk.
That is unlikely to change with the new government.
Almost two thirds of the fund's assets were held in equities at the end of the second quarter, giving it control over 1.3 percent of all globally listed stocks.
By contrast, Norway's population of 5.3 million people corresponds to less than 0.1 percent of the world's population.
By 1148 GMT, the fund's value had again dipped slightly below the trillion-dollar mark, standing at $998 billion. ($1 = 7.8473 Norwegian crowns) (Editing by Angus MacSwan and Alexander Smith)