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* All three major U.S. stock indexes in the black
* European, emerging equities markets rally
* Pound rises after PM Johnson's setback in parliament
* U.S. Treasury yield curve steepens as long-dated yields rise
* Hong Kong scraps extradition bill, boosting sentiment (Updates to afternoon, adds graphic and story links)
NEW YORK, Sept 4 (Reuters) - Stocks rebounded worldwide on Wednesday, and the U.S. Treasury yield curve steepened as easing geopolitical concerns and upbeat economic data from China helped revive investor risk appetite.
A parliamentary vote in Britain raised hopes that the nation's no-deal exit from the European Union could be postponed, Hong Kong withdrew the contentious extradition bill at the heart of recent protests and political risks in Italy appeared to be easing, all of which brought buyers back to equities markets.
China's services sector expanded in August at its fastest pace in three months as a jump in new orders prompted the biggest hiring increase in over a year, according to the Caixin/Markit services purchasing managers index (PMI).
"Geopolitics are lifting everything much in the way it drowned everything yesterday," said Paul Nolte, portfolio manager at Kingsview Asset Management in Chicago. "It's as if the slate gets wiped clean and we're starting from zero every day."
"The markets are very binary," Nolte added. "It's either 'happy days are here again' or 'things are terrible and we're falling into the abyss."'
The U.S. trade deficit shrank in July, according to the Commerce Department, but bilateral gaps in goods trade with key trading partners widened. The closely watched deficit with China grew by 9.4% as the bruising Sino-U.S. trade war raged on and the deficit with the European Union hit a record high.
The Dow Jones Industrial Average rose 212.06 points, or 0.81%, to 26,330.08, the S&P 500 gained 27.56 points, or 0.95%, to 2,933.83 and the Nasdaq Composite added 94.49 points, or 1.2%, to 7,968.64.
The political developments in Europe and Hong Kong helped fuel a rally in European stocks, sending them to one-month highs.
The pan-European STOXX 600 index rose 0.89% and MSCI's gauge of stocks across the globe gained 1.10%.
Emerging market stocks rose 1.86%. MSCI's broadest index of Asia-Pacific shares outside Japan closed 1.82% higher, while Japan's Nikkei rose 0.12%.
The U.S. Treasury yield curve was at its steepest in two weeks as improving risk sentiment sent longer-dated yields edged higher.
Benchmark 10-year notes last rose 3/32 in price to yield 1.4556%, from 1.466% late on Tuesday.
The 30-year bond last fell 4/32 in price to yield 1.9552%, from 1.95% late on Tuesday.
Fresh doubts about the scale of the European Central Bank's stimulus caused the euro to rebound, while the dollar continued its retreat from a more than two-year high against a basket of major world currencies. The pound sterling recovered as efforts to stop a no-deal Brexit advanced.
The dollar index fell 0.51%, with the euro up 0.46% to $1.1023.
The Japanese yen weakened 0.33% versus the greenback at 106.30 per dollar, while sterling was last trading at $1.2205, up 1.00% on the day.
Oil prices rose with the tide, with WTI crude on track for its biggest daily percentage increase since June 10, boosted by easing geopolitical tensions and the positive news about China's services sector.
U.S. crude rose 4.54% to $56.39 per barrel and Brent was last at $60.79, up 4.34% on the day.
Gold inched higher amid remaining economic concerns in the shadow of the U.S.-China trade, but the precious metal still hovered below its six-year peak.
Spot gold added 0.3% to $1,551.80 an ounce.
Copper rose 2.53% to $5,752.00 a tonne.
Three-month aluminum on the London Metal Exchange rose 1.06% to $1,771.50 a tonne.
(Reporting by Stephen Culp Editing by Nick Zieminski)