* Europe's big economies see no improvement going into Q4
* PMIs show economic contraction worsening in Oct
* Surveys show scant hope of turnaround soon
* Ireland, Italy represent few bright spots
LONDON, Nov 6 (Reuters) - The fourth quarter has so far brought no improvement in the fortunes of most of Europe's economies, which now risk shrinking more than previously expected, surveys showed on Tuesday.
Purchasing managers indexes (PMIs), which gauge the activity of thousands of companies worldwide, showed euro zone businesses endured their worst month in October since June 2009, with little hope of a turnaround coming soon.
The euro zone relies heavily on Germany, its largest economy, to generate growth. Business activity there shrank at faster pace last month.
Survey compiler Markit said the latest PMI was consistent with the euro zone economy shrinking at a quarterly rate of around 0.5 percent.
If the PMIs fail to improve for November and December, the euro zone economy could easily face a hefty contraction in the fourth quarter rather than the stagnation projected by economists polled by Reuters two weeks ago.
``Given the stabilisation in financial markets, and in consumer sentiment indicators in some countries, we thought perhaps you would see some stabilisation in the PMIs as well,'' said Janet Henry, chief European economist at HSBC.
``What's disappointing about the Q4 data is the weakness reflected in the core euro zone indicators -- the French and German PMIs.''
There were two bright spots in Tuesday's data. The Irish survey rebounded strongly in October and the Italian services PMI, while still showing businesses are struggling, shot above the highest forecast from economists.
``It's not all really bad news, but it's all consistent with a contraction in the real economy. And that's not what you want when you've got really high debt levels,'' said Henry.
That applies particularly to Spain, the euro zone's No.4 economy, as its services sector shrank for a 16th straight month. Most say it's only a matter of time, likely before the end of the year, that Spain asks for a full sovereign bailout.
The European Commission has set dire economic forecasts for Spain until 2014, a newspaper reported on Tuesday, shooting down the targets set out by Madrid and potentially pushing it closer to seeking euro zone aid.
Markit's Eurozone Composite PMI fell in October to 45.7 from 46.1 in September, down slightly from a preliminary reading of 45.8 two weeks ago and marking its ninth consecutive month below the 50 mark dividing growth from contraction.
The survey will do little to alter the view of a majority of economists that the European Central Bank will trim interest rates to a new record low of 0.5 percent, although probably early next year rather than this Thursday.
``Sentiment is still being hit hard as companies worry about the dual impact of weak domestic demand and a slowing global economy,'' said Rob Dobson, senior economist at PMI compiler Markit.
Surveys from Asia and the United States released on Monday suggested the euro zone will remain the global economy's principal laggard going into 2013.
Britain's services PMIs were released on Monday, and suggested its economy slowed much more than expected in October.
That compounded a PMI last week that showed UK manufacturing slumped badly in October, ending a run of more hopeful data on the economy.
British industrial output also fell more sharply than expected in September.