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European shares steady around 5-1/2 year highs, Fiat surges

* FTSEurofirst 300 flat

* Fiat jumps 15 pct after deal to buy Chrysler

* Index touches highest levels since 2008 in early trade

By Alistair Smout

LONDON, Jan 2 (Reuters) - European shares touched fresh 5-1/2 year highs on Thursday, making a steady start to the new year after rounding off 2013 with their best annual performance in four years.

Fiat FIA.MI> helped to support the market on Thursday, surging 15 percent after the Italian carmaker gained full control of Chrysler.

Its shares traded in heavy volume of 1.7 times their 90-day average after the company tied up a deal to buy the remaining 41.46 percent of the American carmaker that it did not already own, after over a year of protracted talks.

Italian investment firm Exor, Fiat's majority stakeholder, rose 6 percent, and the two stocks were the FTSEurofirst 300's first and second top gainers.

The pan-European index was flat at 1,316.32 after hitting fresh 5-1/2 year highs in early trade. The FTSEurofirst rallied 16.1 percent in 2013 in its best showing since 2009 thanks to ample liquidity from global central banks and early signs of an economic recovery in Europe.

Sentiment remained supported by the strong gains enjoyed over 2013 and a 6.1 percent rally since the middle of December.

A touch of caution to the new year's trading was added by news that China's factory activity slowed in December, raising concern about the strength of demand in the world's second-biggest economy.

However, market attention was on whether there was the conviction to push on and make fresh highs in what was expected to be a light trading session, with many investors yet to return to work after the Christmas and New Year holidays.

"We're looking to see a continuation from last year's trend, rather than any focus on the data from China overnight," David Madden, analyst at IG, said.

"(However), people are still in holiday mode, and it might not be before next week that we see volume come back to the market."

Historically, equities have enjoyed gains in early January as investors put on fresh bets for the year ahead. A Reuters poll at the end of 2013 forecast a 12 percent gain for European stocks in the coming year.

The first trading month of the year has been positive every month since 2010.

"January is normally a very strong month, you always see very strong bids in the market this time of year," said Peter Garnry, equity strategist at Saxo Bank.

"It has been quite an incredible rally and at some point I think we will need to see a correction, but it probably won't be in January."