* Spain's 10-year bond yield hits all-time low
* Socialists' Sanchez quits as leader
* Lifts hopes that political stalemate close to end
* Attention turns to risks facing Italy, Portugal (Updates prices for close)
By Dhara Ranasinghe
LONDON, Oct 3 (Reuters) - Spain's 10-year bond yield touched a record low on Monday, outperforming most other euro zone peers on hopes that the resignation of the Socialist party leader at the weekend would pave the way for the formation of a new government.
Low-rated euro zone debt started the final quarter of the year broadly backfoot as the focus turned to looming risks in the peripheral euro zone states. There were also renewed worries about the fallout from Brexit on news that Britain will trigger the process to leave the European Union by the end of March.
The leader of Spain's Socialists, Pedro Sanchez, resigned on Saturday after losing a vote triggered by a party revolt, a step that could end a nine-month political deadlock.
Sanchez had been in a stand-off with acting Prime Minister Mariano Rajoy's People's Party, frustrating efforts to form a government after two elections left the conservatives with the most votes but shy of a majority.
The Spanish constitution allows for another attempt to form a government by the end of October and if that is unsuccessful, a third election will be called in December.
"It's not clear that the Socialist party will abstain in another vote by Rajoy to form a government, but markets have taken the resignation of Sanchez well," said Mizuho strategist Antoine Bouvet.
Spain's 10-year bond yield fell almost 2 basis points to a record low at 0.865 percent, before pulling back to 0.91 percent as Italian and Portuguese bonds came under pressure.
Italian 10-year bond yields were 5 bps higher on the day at 1.25 percent IT10YT-TWEB, while Portuguese yields rose 4 bps to 3.39 percent.
German Bund yields were up 2 bps at minus 0.10 percent with trading subdued due to a public holiday in Germany.
A decision by ratings agency S&P to affirm Spain's BBB+ credit rating with a stable outlook late on Friday helped to lift sentiment towards Spanish bonds since some banks had highlighted the risk of a downgrade to the outlook.
S&P said the stable outlook reflected a view that momentum in the economy would continue.
Spanish manufacturing activity grew in September at the fastest rate since April, a survey showed on Monday, with new orders expanding rapidly.
The country's relative economic strength and hopes that the political impasse will be resolved soon contrasts with growing concerns about neighbouring peers Italy and Portugal.
Italian Interior Minister Angelino Alfano at the weekend looked to calm fears about political stability, saying the government will not resign whatever happened in a forthcoming referendum on constitutional reform.
Italy's Baa2 rating is due for a review by Moody's on Friday and Commerzbank says that the stable outlook could be at risk.
In Portugal, jittery markets are counting down to a review on Oct. 21 by DBRS, the last major ratings agency to give Portugal the investment grade rating it needs to qualify for the European Central Bank's bond-buying programme.
DBRS warned in August that pressures were building on Portugal's creditworthiness.
Portuguese bond yields rose about 28 bps in September, posting their biggest monthly rise sine June 2015.
"Portugal ended Q3 on a weak footing and it's now October and we have a key DBRS review coming up," said Commerzbank rates strategist David Schnautz. (Reporting by Dhara Ranasinghe; editing by Mark Heinrich)