The wind of change which Alex Salmond claimed was blowing through Scottish politics is still going strong. Breezing through council chambers up and down the land, it is casting old Labour administrations aside as the SNP takes power, in many cases where they had previously been, at best irrelevant, at worst non-existent.

The Nationalists increased their quota in 29 councils and are now the largest group - or largest equal - in 10 authorities.

Aberdeen, Argyll and Bute, East Lothian, Edinburgh, Highland, Renfrewshire and West Lothian all now have SNP councillors involved in a ruling coalition.

An SNP-led deal is imminent in East Dunbartonshire and possible in the three Ayrshire councils, in South Lanarkshire, West Dunbartonshire and Stirling. In these, some would involve the Tories, which is officially against SNP policy.

The position is a far cry from the past four years, where they had but one council, Angus, and were onlookers in most of the coalition deals.

Decades of Labour domination is crumbling in places where the "monkey in a red rosette" joke was still credible until Thursday, May 3.

From having overall majority control of 12 councils last time round, Labour ended with only two, Glasgow and North Lanarkshire. In both, they now have significant oppositions to contend with after years of massive majorities. Yesterday, they managed to retain the leader and deputy leader of North Ayrshire in a minority administration.

Proportional representation has translated the SNP vote into seats for the first time. In 2003, they won 24% of the council vote but gained only 181 councillors, just 15% of the total.

This time round, however, they increased their vote to just less than 30%, which gave them 30% of the seats, allowing the SNP to emerge as the biggest party in local government with 363 councillors.

Professor Richard Kerley, of Queen Margaret University in Edinburgh, whose report recommended the single transferable vote system for the elections, said the SNP got their tactics spot on.

He said: "The SNP had a good campaign for local government. It was shrewd in how many people it put forward and was successful in securing a higher proportion of candidates elected, in some cases a clean sweep.

"I assume as a party they have made an internal decision, in that they try to get into power where they can. The national rhetoric of who they won't deal with is going out the window; there are deals involving Tories in Edinburgh and West Lothian. In many councils, the idea of one party in control is no longer tenable."

In many authorities, after years of opposition in the face of a seemingly invincible common enemy, the other parties seem eager to coalesce with the burgeoning SNP groups to expel Labour from power.

In Edinburgh, Renfrewshire and East and West Lothian, Labour has lost power, even though in the latter it still emerged as the biggest party.

Liberal Democrats, Conservatives, Independents and single-issue campaigners grasped the opportunity and have left some Labour councillors seething at deals being done to exclude them from power.

In Edinburgh, 17 LibDem councillors joined 12 SNP, leaving them one short of a majority, but support from the 11 Tories will allow them to elect a leader and a provost and form the administration, pushing the 15 Labour councillors into opposition.

Labour group leader Ewan Aitken said: "The new proportional election system, by its very nature, decrees that coalition government is the order of the day. It means all political parties in Edinburgh must adjust to this new political reality and seek common purpose and agreement for the sake of the city. The Labour Party, who delivered PR, saw this as an opportunity to create a new type of politics."

In West Lothian, a deal was forged between the 13 SNP and three St John's Hospital campaigners. With the support of a single Tory, John Kerr, which earned him the title of Provost, they pushed the 14 Labour councillors into opposition.

Graeme Morrice, Labour group leader, was outraged. He said: "We did not get a kicking. Mr Salmond said the SNP as the largest party has the moral right to govern.

"Well, if it is good enough for Holyrood, it is good enough for West Lothian. We got more votes. The people of West Lothian didn't want the SNP."

James Mitchell, professor of politics at Strathclyde University, said Labour has a hard lesson to learn: "There is a kind of pattern emerging but with some local differences. I suspect in those areas where Labour was the largest party, those who have been out of office have had a common cause - to get in.

"There has been a dog fight in Edinburgh between Labour and LibDems for years, so we shouldn't be surprised at that decision. The party in power is there to be challenged."

He added: "Over the past eight years, Labour has been a minority party but has been accepted as the biggest party in terms of seats. Others have been irritated by a perceived arrogance from Labour.

"It is now minority politics which requires a different style of working, in a consensual manner. Labour can no longer control Scotland. It has to come back as a different kind of party, as local government changes will be as significant as the parliament."

After the results were announced, the SNP was celebrating the breakthrough for which they had been waiting decades.

Deputy leader Nicola Sturgeon said: "These figures underline the extent of the SNP's success. The SNP are now the largest party in Scottish local government. After a generation, Labour's one-party states are history.

"There has been a seismic shift in Scottish public life, and councils will benefit from full democratic accountability."

Most of the councils have still to be decided. They have until May 24 to elect leaders. Many are meeting today and others just days before the deadline next week, with talks continuing among the various parties.

Dumfries and Galloway yesterday failed to reach an agreement at the first full council meeting since the election, and will try again next week.

The full effect of proportional representation on the local government map will not be known until late next week.