By Robin Emmott

BRUSSELS (Reuters) - NATO leaders meet in Warsaw on Friday to cement a new deterrent against what they see as an emboldened Russia, returning to Cold War-style defense with Washington again taking the part of Europe's protector.

Britain's decision to quit the European Union, along with a migration crisis and Islamic militancy, leaves U.S. President Barack Obama seeking a show of unity at his last alliance summit to fend off accusations that NATO is obsolete and to dampen any Russian perceptions of weakness in the Western camp.

"The NATO summit was not supposed to be about Britain," said Ian Bond at the Centre of European Reform think-tank in London. "But NATO leaders will not be able to ignore the security implications of Britain's vote to leave the EU," he said.

Even with such a proliferation of issues, including a resurgent Taliban in Afghanistan and Iran's ballistic missile arsenal, the two-day summit will be dominated by NATO's response to Russia and a conflict in Ukraine that the West accuses Moscow of fomenting at a cost of more than 9,000 lives.

Russia says it is the alliance, not Moscow, that is increasing the risks of a broader conflict in Europe, citing NATO's biggest modernization since the Cold War and a U.S. missile defense shield as reasons to be worried.

TRIP WIRE FORCE?

NATO's modernization is crystallizing around a new force in the Baltics and Poland of up to 4,000 troops to serve as a constant reminder to Moscow that the alliance is back to its founding mandate of defending its territory, after years of missions beyond its borders.

"We're in a new relationship with a newly aggressive, newly assertive Russia," said Douglas Lute, Washington's envoy to NATO. "It's brought us back to the primacy of our initial core task: collective defense, our immediate neighborhood."

In Warsaw, the United States, Canada, Germany and Britain will step up to lead the four battalions on the eastern flank.

The deterrent will also be made up of a new network of eight small NATO outposts, more war games, and, if needed, a rapid response force, including air, maritime and special operations components of up to 40,000 personnel.

Air defenses in the Baltics, a strategy against potential Russian cyber attacks and a NATO presence in the Black Sea, where Russia has a fleet, will also be strengthened over time, NATO diplomats say.

While dismissed as merely a trip wire by some military experts, NATO says the battalions reassure the ex-Soviet countries in Europe that they are protected from the kind of annexation Russia orchestrated in February 2014 in Crimea.

NATO also avoids a return to the Cold War, when the United States had 300,000 service personnel stationed in Europe, and allows the alliance to respect a 1997 agreement with Russia not to put large numbers of troops permanently on NATO's borders.

PIVOT ... BACK TO EUROPE

Still, the United States will be providing much of NATO'S deterrent, with warehoused U.S. equipment in Germany ready for any conflict, its battalion of around 1,000 soldiers in Poland and an armored brigade moving around central Europe.

That puts Washington back in its post-World War Two role of defending its European allies, despite Obama's efforts to refocus U.S. attention on the growing economies of Asia and to encourage Europe to take care of its own neighborhood.

"It's like trying to leave the Mafia," said one senior Western defense official of Obama's November 2011 'pivot to Asia' and away from Europe. "Just when you thought you were out, they pull you back in," said the official, paraphrasing a famous line from the American movie trilogy "The Godfather".

With Europe's credibility under threat and with Britons voting to leave the European Union, Washington will confront allies over their military spending at the summit, in what one NATO diplomat described as a "naming and shaming" exercise.

Although European defense spending is increasing after years of cuts, Donald Trump, the presumptive Republican presidential nominee, says allies are "ripping off" the United States and that NATO countries are "not paying their fair share".

Missile defense is another sensitive area at the summit. Part of the U.S. response to protect against Iranian missiles, Russia blames the United States for raising the stakes, convinced the shield is aimed at disabling its nuclear warheads.

The United States, which says its system is not capable of downing its missiles, wants to hand over command and control of the missile shield to NATO at Warsaw.

But France, which is leading diplomatic efforts for an end to the conflict in Ukraine, has been reluctant for NATO to take responsibility for the missile shield given the anger it arouses in Moscow and is concerned about who presses the button in the event of an interception.

"We have very little time to decide when we face a possible attack," said NATO Secretary-General Jens Stoltenberg. "We have to find ways to ensure the necessary political control."

(Reporting by Robin Emmott; editing by Ralph Boulton)