* U.S. futures, European shares gain as election outcomes in line with expectations
* Trade worries likely to remain despite Democrats' win
* Dollar tumbles 0.4 pct, US yields fall on stimulus doubts
* Midterm election interactive tmsnrt.rs/2D6XH9t (Updates throughout, changes byline dateline)
By Sujata Rao
LONDON, Nov 7 (Reuters) - Wall Street was set for a modestly firmer open on Wednesday and global stocks rose after significant U.S. election gains for the opposition Democrats, but the outcome may rule out further tax cuts, sending the dollar and Treasury yields sharply lower.
The Democrats look headed to gain more than 30 seats, well beyond the 23 they needed to claim their first majority in the House in eight years. With President Donald Trump's Republican party holding onto its Senate majority, the results from Tuesday's elections were in line with expectations.
Moreover, while gridlock in Washington could hamper Trump's political and economic agenda, few expect a reversal of tax cutting and financial deregulation measures that have already been enacted.
That view helped all three New York equity indexes to rise around 0.7 percent on Tuesday and they looked set to build on those gains, with S&P500 and Nasdaq futures up 0.7 percent and 1.25 percent respectively .
Market sentiment had been volatile in Asian trade with stocks and the dollar swinging on the Republicans' fluctuating prospects of retaining the House. But by 0900 GMT, MSCI's world equity index was up 0.3 percent, while a pan-European stocks benchmark jumped around one percent .
"The good news in a way for markets is that there was an uncertainty that's now been removed. We know where we stand for the next two years and investors will focus back on the fundamentals which are (company) earnings growth and the economy," said Guy Miller, chief market strategist at Zurich Insurance Group.
On the other hand, most agree the newly empowered House Democrats will have the ability to investigate Trump's tax returns, possible business conflicts of interest and allegations involving his 2016 campaign's links to Russia.
Moreover, a split Congress will be able to hamper Trump's push for a further round of tax cuts and deregulation - measures that have turbo-charged the U.S. economy, stock markets and the dollar, keeping the Federal Reserve on a policy-tightening path.
The Fed is expected to signal this week that an interest rate rise remains on the agenda for December.
"Certainly it is now unlikely we will see additional fiscal stimulus in the near-term, that's a profound change but there will be no repeal of what's already in place," Miller said.
That view pushed the dollar 0.4 percent lower against a basket of currencies. Against the yen, it was 0.4 percent lower at 113.06, reversing earlier gains to a one-month high of 113.82 yen.
The euro rose almost half a percent to $1.148 a two-week high, while the British pound gained 0.4 percent to $1.315, clinging to three-week highs hit after Brexit Secretary Dominic Raab indicated on Tuesday that a deal on exiting the European Union was likely.
On bond markets, ten-year U.S. Treasury bond yields fell below 3.18 percent, down four basis points on the day as it became clear that more fiscal stimulus was unlikely.
An initial knee-jerk rise to 3.25 percent came after early reports of a better-than-expected performance by the Republicans, but that move soon fizzled as results trickled in.
The bond market may remain under pressure from this week's record volumes of longer-dated government debt supply and the yawning Federal deficit. Many also reckon more spending increases are still possible.
"There are still areas with compromise for spending, so even with a split government I expect more fiscal stimulus ahead. There is some possibility for compromise on infrastructure spending as well," Steve Friedman, a senior economist at BNP Paribas Asset Management, said.
Attention will also focus on Trump's hard line on trade tariffs, which he can impose without Congressional approval. That keeps alive worries about a trade war between China and the United States.
Chinese shares closed 0.7 percent lower, while Hong Kong markets ended just above flat
"We would argue that if Trump can do less on the domestic front he is more likely to focus on external matters such as trade, which will impact risk sentiment," said Patrick O'Donnell, investment manager at Aberdeen Asset Management in London.
Oil prices were soft after a 2 percent fall the previous day, with Brent crude futures down 0.25 percent to just below $72 a barrel. (Additional reporting by Hideyuki Sano in Tokyo; Tomo Uetake and Daniel Leussink in Tokyo, Daniel Bases in New York; Editing by Andrew Heavens)