* Years of stimulus raised questions over Fed's control
* Borrowing costs up in relatively calm Libor, repo markets
* Fed awards modest $105.2 bln in smooth repo auction (Adds links to graphics)
By Richard Leong and Jonathan Spicer
NEW YORK, Dec 17 (Reuters) - The Federal Reserve absorbed a modest $105.2 billion in bids on Thursday in a critical auction meant to help raise U.S. interest rates for the first time in nearly a decade, while around the world borrowing costs jumped in a welcome sign for the U.S. central bank.
The relatively calm market reaction came as an early relief for the Fed, which is using new tools to mop up trillions of dollars in excess cash flooding the financial system after years of efforts to stimulate the U.S. economy.
One of those tools, the mid-day auction for overnight reverse repurchases, attracted bids from 49 money funds, banks and other firms. The facility has been tested for more than two years and stood ready to absorb up to $2 trillion in bids, even though the interest on Thursday was in line with recent weeks.
Other short-term markets appeared to cooperate with the Fed's intention to make money modestly more expensive for the first time since the 2007-2009 financial crisis.
Libor, a global rate benchmark for $350 trillion worth of securities and loans, booked its biggest single-day rise since May, 2010, while a key borrowing cost for Wall Street firms more than doubled.
Moves in the short-term Treasury markets were modest, the dollar rose as expected, and world stocks climbed then declined the day after the Fed's well-telegraphed move.
"The Fed has to be patting themselves on the back given what's happened in markets," said Andrew Szczurowski, portfolio manager at Eaton Vance, in Boston. "With all of their transparency they managed to pull any volatility forward (before the hike), so I'd say it's a success."
The world's most influential central bank decided on Wednesday to raise its key policy rate modestly to a new range of 0.25 to 0.5 percent, in a nod to U.S. labor market strength and the expectation that inflation is around the corner.
The heavy lifting began on Thursday and will continue in the weeks and months ahead as the Fed uses new tools to pry borrowing costs off the floor. After seven years of near-zero rates and unprecedented bond buying, banks are flooded with some $2.6 trillion in excess reserves that makes it far more difficult than in the past to lift rates.
To ensure they rise as much as desired, the Fed effectively ditched a cap on the so-called overnight reverse repurchase program, or ON RRP, saying on Wednesday it would use as many of its Treasury bonds as needed for the daily auctions.
The reverse repo facility was previously capped at $300 billion in what was largely a test phase. Analysts, who had mostly expected the Fed to only double the facility, applauded Thursday's results.
"This shows the ease for the Fed to move the federal funds rate without pushing too many levers," Aaron Kohli, interest rates strategist at BMO Capital Markets, said of the target rate that is to remain in the 0.25 to 0.5 percent range.
The Fed's 30-minute auction attracted only muted interest because higher returns were available elsewhere in the broader $5-trillion repo market.
There, the overnight rate for Wall Street banks to borrow from money market funds and other cash investors rose to 0.43-0.47 percent, from 0.20 percent late Wednesday , according to ICAP data.
Major U.S. banks had earlier raised their prime rates, a benchmark for consumer and commercial loans, for the first time in nearly a decade to 3.5 percent from 3.25 percent.
Meanwhile the Libor measure of interbank borrowing costs rose 0.04 percent. But it is up more than 0.20 percentage point since November as investors anticipated the U.S. rate hike, and as lending diminished toward year-end.
While trading was relatively muted, the real test for the Fed may come as market liquidity dries up and investors close down trading positions toward year end. Banks also curb short-term lending on the last day of the quarter.
"It could be well into January before the Fed gets the daily amount of the RRP program perfectly calibrated," said Carl Tannenbaum, chief economist at Northern Trust and a former Chicago Fed official.
From its "operations room" three blocks off Wall Street, traders at the New York Fed set the reverse repo rate at 0.25 percent, up from 0.05 percent. It will serve as the "floor" to the new target policy range while a rate the Fed pays primary dealers on excess reserves, also a relatively new tool, will serve as the "ceiling" at 0.5 percent.
Also on Thursday, rate futures markets slipped as traders expected the Fed would follow up with another rate increase by mid-2016.
Reporting by Richard Leong and Jonathan Spicer in New York; Additional reporting by Dhara Ranasinghe in London; Editing by Nigel Stephenson and Chizu Nomiyama