* Asia shares highest since late 2007, Japan on holiday
* Dollar gains on broadly softer yen ahead of Fed meeting
* Fed likely to announce gradual unwinding of balance sheet
* Yields on the rise as central banks sound hawkish
SYDNEY, Sept 18 (Reuters) - Asian shares hit decade highs on Monday and the dollar gained on the yen early in a week in which the U.S. Federal Reserve is likely to wrestle with its bloated balance sheet as part of a long reversal of super-cheap money worldwide.
European and U.S. stocks looked set to echo those gains, with Eurostoxx 50 futures up 0.46 percent and the FTSE 0.43 percent, while E-Mini futures for the S&P 500 rose 0.25 percent.
There was relief the weekend passed with no new provocation by North Korea, though Pyongyang's nuclear ambitions will be center stage when U.S. President Donald Trump addresses world leaders at the United Nations on Tuesday.
Some details of Trump's tax reform plans may also emerge this week, while elections in Germany and New Zealand will add extra political uncertainty to the mix.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.9 percent to reach heights not visited since late 2007.
Samsung Electronics led the gains to reach an all-time top as global demand for hi-tech gadgets remains strong, while healthcare and financial stocks also drew buyers.
Australia's index added 0.5 percent while Japan's Nikkei was closed for a holiday.
For markets, the main event will be the Fed's meeting on Tuesday and Wednesday, where it is likely to take another step toward policy normalization amid what is rapidly becoming a global trend.
Canada has already hiked twice in recent months and the Bank of England shocked many last week by flagging its own coming increases.
Yet investors are far from convinced the Fed will move on rates again this year, with December put at less than a 50 percent probability in the futures market.
"It is fair to say that in our recent travels most of the investors we have spoken to question not just a December hike, but whether the Fed will hike at all again this cycle," said Tom Porcelli, chief U.S. economist at RBC Capital Markets.
"When you press investors on the why, the standard reply is the lack of inflationary pressures."
Porcelli, however, argued the market was underestimating the risk of tightening and predicted not only a hike in December but four more over 2018.
Yields on U.S. 10-year Treasuries did jump a hefty 14 basis points last week, and still trailed the UK where yields on 10-year paper surged 30 basis points.
The seismic shift in rates saw sterling hit its highest since the Brexit vote and notch its best week in almost nine years against a currency basket.
On Monday, the pound was a shade softer at $1.3585 but not far from the peak of $1.3615. The euro was steady at $1.1945, sandwiched between support at $1.1836 and resistance at $1.2092.
The dollar held firm on the yen at 111.20, with the Bank of Japan widely expected to maintain its massive asset buying campaign at a meeting on Thursday.
Political uncertainty also made a surprise appearance after sources said Japanese Prime Minister Shinzo Abe was considering calling a snap election for as early as next month to take advantage of his improved approval ratings and disarray in the main opposition party.
Against a basket of currencies, the dollar was idling at 91.869 and still uncomfortably close to the recent 2-1/2 year trough of 91.011.
The modest bounce in the dollar combined with all the talk of monetary tightening put gold on the defensive. The precious metal was off 0.1 percent at $1,317.78 an ounce.
Oil prices were hovering near five-month highs helped by a fall in the number of U.S. rigs drilling for new production and as refineries continued to restart after getting knocked out by Hurricane Harvey.
Brent crude was up 7 cents at $55.69 a barrel, following gains of 3.3 percent last week. U.S. crude firmed 7 cents to $49.97 a barrel.
(Reporting by Wayne Cole; Editing by Richard Borsuk and Kim Coghill)