* Caution as voting starts in UK referendum supports Bunds
* Two polls published late Wednesday give "Remain" camp a lead
* Volumes thin
* Greece in focus as ECB takes Greek banks off emergency lifeline
By Dhara Ranasinghe
LONDON, June 23 (Reuters) - A sense of caution as voting kicked off in a tight referendum on the UK's membership of the European Union bolstered safe-haven German bonds on Thursday, as latest polls showed a slight tilt towards those in favour of keeping Britain in the EU.
Sterling rose to its strongest this year against the dollar after two polls showed a swing to "Remain" and betting markets priced in an 80 percent chance Britain would not vote to leave the EU.
As momentum shifted towards the remain camp over the past week, risk appetite has picked up in global markets - benefiting lower-rated southern European debt at the expense of top-rated German bonds. European shares were broadly higher on Thursday.
But with the vote too close to call, caution gripped bond investors, keeping Germany's 10-year government bond yield, the benchmark for borrowing costs in the euro area, within 10 basis points of record lows hit last week.
"We have a poster on our trading floor which shows Bart Simpson writing never sell Bunds repeatedly," said David Schnautz, interest rate strategist at Commerzbank, referring to the cartoon character from the show, The Simpsons. "And on a day like this, you have to ask do you want to sell German bonds?"
The German 10-year bond yield was down 2 basis points at 0.05 percent, while 30-year bonds yields fell 3 bps to 0.64 percent.
Goldman Sachs expects a "Remain" outcome to push German Bund yields up by around 10 bps, while a "Leave" vote could push yields to minus 0.01 percent.
Other euro zone bond yields were 1-2 bps lower, in light trading volumes.
Peter Chatwell, head of European rates strategy at Mizuho, said government bond markets in Europe currently price in a higher probability of a remain vote.
He said a vote in favour of leaving the EU could see the 10-year yield gap between Italian and German bonds widen by 27 bps and tighten by 15 bps if remain wins.
The yield gap stands at around 151 bps, its tightest in more than a month.
Peripheral bond markets are seen as especially vulnerable to the political and economic fallout of a Brexit vote.
Italy's anti-establishment 5-Star Movement, buoyed by big gains in local elections, has pressed demands for a referendum on whether to keep the euro, something that would add to a wave of plebiscites shaking politics across Europe.
Elsewhere, Greece was in focus after the European Central Bank reinstated Greek banks' access to its cheap funding operations on Wednesday after more than a year on an emergency lifeline. The ECB also said it would examine later whether to add Greek debt to its asset purchases.
For Reuters new Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http:// emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarket s (Reporting by Dhara Ranasinghe; Editing by Toby Chopra)