* Asian stock markets : tmsnrt.rs/2zpUAr4
* Wall St advance, dollar flat as traders brace for a dovish Fed
* Pound choppy as UK parliament bans vote on same Brexit deal
By Tomo Uetake
March 19 - Asian shares treaded water on Tuesday ahead of a U.S. Federal Reserve policy meeting, hovering near six-month highs, while sterling was choppy as the speaker of Britain's parliament banned another vote on same Brexit deal.
MSCI's broadest index of Asia-Pacific shares outside Japan was virtually flat, just a hair away from the highest level since Sept. 21.
Japan's Nikkei average dropped 0.5 percent, while Australian stocks eased 0.1 percent.
All three major U.S. indexes rose overnight, lifted by banks and tech names, with the Dow Jones Industrial Average, the S&P 500, and the Nasdaq Composite adding between 0.3 and 0.4 percent each.
"Speculators appear to be betting on rise in stock prices on the back of a dovish Fed. The Fed is unlikely to kill such hopes. Yet there is a risk the Fed could tone down its dovishness," said Masanari Takada, cross-asset strategist at Nomura Securities.
With signs of global economic growth slowing, traders were focused on the Federal Reserve, which is kicking off its two-day policy meeting on later in the day, for clues about the likely path of U.S. borrowing costs.
In particular, investors will be focusing on whether policymakers have sufficiently lowered their interest rate forecasts to more closely align their "dot plot", a diagram showing individual policymakers' rate views for the next three years.
Also expected is more detail on a plan to stop cutting the Fed's holdings of nearly $3.8 trillion in bonds.
"A key focus is when the Fed will omit the word 'patient' from its statement, as that would be a pre-requisite for a rate hike," said Toru Yamamoto, chief fixed income strategist at Daiwa Securities.
In the currency market, the pound found firmer footing on Tuesday after slipping to as low as $1.3183 overnight as lawmakers cast doubt on Prime Minister Theresa May's third attempt to get parliament to back her Brexit deal.
May's Brexit plans were thrown into further turmoil on Monday when the speaker of parliament ruled that she could not put her divorce deal to a new vote unless it was re-submitted in fundamentally different form.
May has only two days to win approval for her deal to leave the European Union if she wants to go to a summit with the bloc's leaders on Thursday with something to offer them in return for more time.
Meanwhile, senior diplomats said the European Union leaders could hold off making any final decision on any Brexit delay when they meet in Brussels later this week, depending on what exactly May asks them for.
The dollar index against a basket of six major currencies barely moved and was at 96.498.
The Japanese yen edged up 0.1 percent to 111.27 yen to the dollar, while the euro was almost flat at $1.1334.
Oil prices rose to near four-month highs on Monday, supported by the prospect of extended OPEC-led oil supply curbs and signs of inventory declines in U.S. crude stockpiles.
Early on Tuesday, U.S. crude futures slipped 0.2 percent to $58.99 a barrel.
Reporting by Tomo Uetake; Additional reporting by Hideyuki Sano; Editing by Kim Coghill