* Scots independence advocates, unionists row over Games
* Games may have contributed to greater national unity
* Team GB Scots reel in medals, Team Scotland unlikely to fare as well
LONDON, Aug 8 (Reuters) - Some call them Scotland's "Scolympians", others say it's Team GB all the way.
An impressive performance by Scots in Britain's Olympic team - third in the medals table - has dragged the world of sport into an Olympian tussle over Scotland's bid for independence.
Scottish athletes have won 11 of Britain's 48 Olympic medals and have matched the German and Italian hauls of seven golds. Not bad for a country of about five million people - just a twelfth of the British population.
The Scottish National Party (SNP), which controls Scotland's devolved government, plans to hold a referendum on secession in 2014, and in a video wishing athletes good luck ahead of the Games SNP politicians pointedly avoid the word "Britain".
"The eyes of the world are on the Olympics and the whole of Scotland is united in supporting our Olympians and Paralympians - our 'Scolympians' - to go for gold," SNP leader and Scotland's First Minister Alex Salmond said.
Unfortunately for Salmond, Scottish tennis star Andy Murray, one of Britain's highest-profile gold medal winners of the Games, draped himself in the Union Jack at his medal ceremony on Sunday, prompting triumphant comments from unionists.
"Andy Murray, great Scot and Olympic Champion, holding a gold medal and proudly draped in the Union Jack - eat your heart out Alex Salmond!" tweeted unionist Conservative lawmaker Struan Stevenson, who represents Scotland in the European Parliament.
"As we watch Andy Murray singing our National Anthem, never forget that there are small-minded Nationalists who want to destroy TeamGB," tweeted Scottish parliamentarian Murdo Fraser.
For his part, Salmond said Murray's win "should make everyone in Scotland extremely proud", while his party labelled unionist gloating as "puerile" attempts to politicise the Games.
"It is a sign of desperation, and they would do better just to watch the Games," the SNP said in a statement.
"100 PERCENT SCOTTISH"
The SNP believes an independent Scotland would be better run and richer. The Edinburgh-based Scottish government runs many public services, but has relatively little control over fiscal issues and no power over foreign affairs and defence.
The SNP won a big election victory in 2011, giving it a clear mandate to pursue its goal of secession, ending the 300-year-old union between Scotland and England.
Britain's three main political parties, which are based in London, oppose Scottish independence, and argue that Scotland is stronger within the union. The parties have united to run a "Better Together" campaign to counter the SNP.
Officials insist they would rise above any attempts to use the Games for political purposes.
"It's not for us to make political points on the back of the Olympics. People can see it for what it is, and that's a great British performance," said Better Together's Rob Shorthouse.
It is difficult to pinpoint what effect the Olympics has had on the debate. A late July YouGov opinion poll put support for independence at 30 percent and opposition at 54 percent, findings little changed from a January survey.
However, it appears that national hysteria as Team GB has reeled in the medals may have contributed to a greater sense of unity and Britishness.
"I think I feel more British," Scott Brash, Scotland's top show jumper told Reuters at the Games, where his team won gold.
"But I'm very passionate about my country and I never forget where I came from. I'm 100 percent Scottish. But it's good that we all work together ... I think it's stronger to be united and that's probably the case for everything, really," he said.
Scottish Olympics spectator Helen Paterson said: "It's been a unifying event. I've noticed a lot of Scottish athletes. It makes me proud to be Scottish and British."
At the Games, which end on Aug. 12, Britain is already celebrating its biggest haul of Olympic gold since 1908, and jubilation has spread across the country, including Scotland.
"I was astonished by the number of people that lined the streets throughout Scotland when the Olympic torch came through," said Nigel Holl, chief executive of scottishathletics, governing body of athletics in Scotland.
"There's fantastic interest in what's going on for Team GB here in Scotland. People are tracking the success of Team GB as a whole and they're tracking the success of Scottish athletes who are part of Team GB with a particular focus," he added.
British media carried headlines such as "Golden success for Olympic Scots" and "Scotland's most successful Olympics ever", inspired partly by Scottish cyclist Chris Hoy, who on Tuesday won another gold to become Britain's most successful Olympian.
But while Scottish athletes may account for many medals, it is unlikely that an independent Scotland, whose population is a fraction of Britain's as a whole, would be quite as illustrious.
"A population of just over five million, compared to 60 odd million for the UK as a whole, yes, it's going to be much harder to be third in the medal table, I don't think anyone would suggest that was even remotely feasible," Holl said.
With the independence ballot two years away, the SNP still has time to whip up nationalist fervour - not least when Scotland competes in the 2014 Commonwealth Games, to be held in the Scottish city of Glasgow. (Additional reporting by Sarah Edmonds, editing by Matt Falloon.)