* European stocks hit session lows after poor U.S. PMI
* German flash manufacturing PMI shows lowest reading in6-1/5 yrs
* Banks, auto stocks post steep falls (Updates to include U.S. PMI data, closing prices)By Susan Mathew and Medha SinghMarch 22 (Reuters) - European stock markets deepened losseson Friday, closing near session lows, as fears of a slowdown inglobal growth after weak manufacturing data from across Europewere exacerbated by dismal data from the United States.After downbeat manufacturing activity from Germany reignitedfears of a recession in the region's biggest economy, theinversion of the U.S. yield curve after similar U.S. data stokedfears that the world's largest economy may also be slipping intorecession.The pan-European STOXX 600 index , which had openedhigher on relief at the extension of Britain's Brexit deadline,slipped for a third day to close down 1.2 percent to take weeklylosses to 1.3 percent - its steepest this year.The London and Paris bourses sank more than2 percent, while Frankfurt and Madrid faredonly slightly better with roughly 1.5 percent declines.The euro zone-wide flash PMI also showed businessesperformed much worse than expected this month, while Frenchbusiness activity slowed unexpectedly.The classic gauge of fear - known as impliedvolatility, which tracks demand for options in European stocks -hit more than 9-week highs and posted its biggest weekly rise ina year, the first concrete sign of activity in a while. Almost all sectors within the STOXX 600 were in the red withbanks , auto and chemicals sectors downmore than two percent each, along with industrial goods andservices stocks . The bank sector posted its biggestdaily drop sine early February.Italian lenders Unicredit , Banco BPM ,and UBI led losses among banks after Credit Suisse saidthe market is underestimating Italian banks' net interest incomechallenges. Nestle , the world biggest food group, was thebiggest drag on the benchmark, down 1.7 percent, followed bymore than 2 percent dips in HSBC Holdings and oil andgas majors Total BP PLC ."With numerous headwinds facing the manufacturing sector inGermany - including a slowdown in the automotive sector, Brexit,U.S.-China trade and a global economic slowdown - there's littleto be optimistic about," said Craig Erlam, senior market analystat Oanda in London.Most European bourses had opened on a stronger footing,relieved at the European Union's agreement to at least atwo-week reprieve that precludes Britain crashing out of thebloc without a deal next week. Despite the relief from the summit overnight, there weremore signs of firms making preparations for a no-deal Brexit, asBritish Prime Minister Theresa May now faces task of persuadinga deeply divided parliament to back her Brexit deal. A no-dealexit could well have a depressive effect on Europe's majoreconomies.Goldman Sachs analysts reduced the likelihood of May's dealpassing to just 50 percent, while raising the chances of"no-deal" to 15 percent. The bank continues to put the chancesof no Brexit at all at 35 percent. The odds of a no-deal exit had fallen to just 5 percent ononline betting market Betfair. (Reporting by Medha Singh, Patrick Graham and Susan Mathew;Editing by Toby Chopra)