* U.S. and European shares gain as election outcomes in line with expectations
* Trade worries likely to remain despite Democrats' win
* Dollar tumbles, U.S. yields fall on stimulus doubts
* Interactive chart on U.S. midterms tmsnrt.rs/2D6XH9t (Changes byline, dateline to NEW YORK; adds Wall Street open; updates throughout)
By Hilary Russ
NEW YORK, Nov 7 (Reuters) - World stocks rose on Wednesday, with Wall Street surging after the U.S. midterm election a day earlier divided control of Congress, but the outcome, which casts doubt on further U.S. tax cuts, hit the dollar and sent Treasury yields lower.
The Democrats looked headed for a gain of more than 30 seats in the House of Representatives, well beyond the 23 they needed to claim their first majority in eight years. With President Donald Trump's Republican party holding on to its Senate majority, the results from Tuesday's election were in line with expectations.
While gridlock in Washington could hamper Trump's political and economic agenda, few expect a reversal of tax cuts and financial deregulation measures that have already been enacted.
That view helped all three Wall Street equity indices open stronger. The Dow Jones Industrial Average rose 213.04 points, or 0.83 percent, to 25,848.05, the S&P 500 gained 27.55 points, or 1.00 percent, to 2,783 and the Nasdaq Composite added 84.49 points, or 1.15 percent, to 7,460.45.
"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.
Interactive chart on U.S. midterms tmsnrt.rs/2D6XH9t
Still, a split Congress could hamper Trump's push for a further round of tax cuts and deregulation, measures that have turbocharged the U.S. economy, stock markets and the dollar.
After volatile Asian trade, where stocks and the dollar swung on the Republicans' fluctuating prospects, the pan-European STOXX 600 index rose 1.02 percent and MSCI's gauge of stocks across the globe gained 0.90 percent.
It was the seventh straight day of gains in global shares.
Riskier European bonds such as those from Italy also were in demand, with yields falling 6-9 basis points.
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 lower against a basket of currencies. The dollar index fell 0.48 percent, with the euro up 0.32 percent to $1.1462.
Ten-year U.S. Treasury bond yields at one point fell to a low of 3.176 percent 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.
"Democrats winning the House is likely to mean slightly less fiscal stimulus going forward. The bond market may take that well because the Federal Reserve will have less work to do," said Richard Buxton, head of UK equities at Merian Global Investors.
Benchmark 10-year notes last rose 6/32 in price to yield 3.193 percent, from 3.215 percent late on Tuesday.
Attention will 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.
The dollar's weakness lifted other currencies. The Japanese yen strengthened 0.11 percent versus the greenback at 113.32 per dollar, while sterling was last at $1.314, up 0.33 percent on the day.
Oil prices reversed their earlier decline after a report that Russia and Saudi Arabia were discussing output cuts in 2019 .
U.S. crude rose 0.69 percent to $62.64 per barrel and Brent was last at $72.83, up 0.97 percent on the day.
Additional reporting by Hideyuki Sano in Tokyo; Tomo Uetake and Daniel Leussink in Tokyo, Daniel Bases in New York, Josephine Mason, Sujata Rao and Dhara Ranasinghe in London; Editing by Bernadette Baum