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* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
* Trump woes leave dollar heading for biggest fall since August
* World stocks index set for first weekly fall in five
* Oil set for second week of strong gains on output curb signals
* Brazil's real reels after worst plunge since 1999 crisis
By Marc Jones
LONDON, May 19 (Reuters) - The dollar limped towards its worst week since August on Friday and world stocks headed for their first weekly fall in five, as storms surrounding Donald Trump's U.S. presidency and Latin America's biggest economy, Brazil, began to calm.
The most eventful week of 2017 for markets started with stocks at record high but then saw one of the sharpest cross-asset routs in years.
Europe's main bourses nudged higher on Friday to build on tentative recoveries on Wall Street and in Tokyo while demand for safe-haven bonds eased.
But jitters persisted, leaving safe-haven gold headed higher again for its best week since April and the dollar back on the slide after falling to its lowest level since Trump's U.S election victory in November.
"The frustrating element is that we are now at the mercy of equity markets," said National Australia Bank's global head of FX strategy, Nick Parsons.
"We can be pretty confident that 10 points on or off of the S&P 500 is a big figure on or off of dollar/yen," he added, saying the only thing likely to break the link would be a confident-sounding Federal Reserve at its next meeting.
The market roller-coaster was triggered by political uproar over Trump's firing of FBI director James Comey and allegations he pressed Comey to stop investigating his former national security chief and his campaign's alleged ties with Russia.
Overlaying that is concern that the resultant political damage could hamper Trump's chances of getting his promised fiscal stimulus -- which has spurred markets higher since November -- through Congress.
The gradual return of risk appetite on Friday also saw investors switch from highly rated U.S. Treasuries and European government bonds into higher-yielding Italian and Portuguese debt.
Like the dollar, the U.S. yield curve has slumped back to levels not seen since Trump's election, and the probability given by markets of the Fed raising rates next month has tumbled to below 60 percent from over 90 percent last week.
"Everything has turned upside down -- European political risks have faded, the economy is looking strong, while in the U.S. everybody is worried," said DZ Bank strategist Daniel Lenz.
It hasn't only been about Trump though. Emerging markets have also been grappling with an unfolding corruption scandal in Brazil that threatens to engulf its president, Michel Temer.
Brazilian markets cratered on Thursday, with stocks down nearly 9 percent and the real 8 percent -- the currency's biggest fall since the 1999 devaluation and crisis, although it looked steadier in European trading.
"For Brazil this is a very serious thing," said Alejo Czerwonko, director of emerging markets investment strategy at UBS. "But in the medium term, the next 3-6 months, this is not necessarily a threat to EM more broadly."
MSCI's main emerging markets index clawed back some ground on Friday but it remained on track for its worst week of the year so far.
In commodities, the story was about supply and demand. Oil was enjoying a third straight session of gains and set for a 4 percent weekly rise following signals that big producer countries may be closing in on a deal to extend output curbs.
U.S. crude futures hit a three-week high, and were last trading up 0.8 percent to $49.76 a barrel. Global benchmark Brent was up a similar amount too at $52.89, near a four-week high.
The U.S. political uncertainty also put a shine on gold. It climbed to $1,248.62 an ounce and was set for a weekly gain of 1.6 percent, which would be its best since April.
"People are still wary of geopolitical risks and not selling the safe-haven asset yet," said Brian Lan, managing director at gold dealer GoldSilver Central in Singapore.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets (Additional reporting by Sujata Rao in London; Editing by Catherine Evans)