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FOREX-Unhedged FX flows pushes euro up for a third day

* Dollar softens as U.S. tax plan progress stalls

* Sterling consolidates gains capping robust week

* Graphic: World FX rates in 2017 http://tmsnrt.rs/2egbfVh

LONDON, Dec 1 (Reuters) - The euro climbed for a third consecutive day on Friday as investment flows propped up the single currency and the region's brightening growth prospects attracted investors despite falling bond yields.

"Even in a week when the dollar has received some positive news from the progress of the U.S. tax plan, the euro seems to be supported by some strong investment flows," said Richard Falkenhall, senior FX strategist at SEB in Stockholm.

The single currency climbed 0.2 percent to $1.926, on track for a third consecutive day of gains. It hit a two-month high of $1.19610 on Monday.

Morgan Stanley strategists said unhedged currency inflows into European stocks have picked up noticeably in recent weeks, pushing up the single currency despite shrinking interest rate differentials.

Investment flows into European assets have picked up at a time when growth prospects have brightened considerably. Business growth is roaring in the final weeks of the year, surveys showed last week.

Elsewhere, the dollar steadied against the Japanese yen on Friday, losing steam after rising to a 10-day high, as the market endured the wait for a vote on a U.S. tax reform bill.

The dollar was last at 112.550 yen, broadly unchanged on the day, after it was decided that the U.S. Senate will not vote on the tax bill late on Thursday night U.S. time but would continue the debate on Friday.

"That fact that the vote did not take place on Thursday evening shows that there are still some kinks to be ironed out, but it is not like the deliberations have fallen through," said Yukio Ishizuki, senior currency strategist at Daiwa Securities.

The dollar index against a basket of six major currencies was 0.2 percent lower at 92.84 but poised to eke out some tiny gains for the week, during which it managed to pull away from a two-month low of 92.496.

The pound was a shade higher at $1.3534 after surging 0.9 percent overnight when it set a two-month high of $1.3549. It was on track to post its best weekly performance since mid-October.

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(Reporting by Saikat Chatterjee; Additional reporting by Shinichi Saoshiro in TOKYO, Editing by William Maclean)