'Battlelines drawn for general election'
The National hails the SNP's victory in the local elections "emphatic", adding that it deals a blow to Theresa May's bid to stop a second independence referendum.
However, the Scottish Conservatives claim a surge in their support has "sunk" a case for a second indy poll, according to The Herald.
The Scotsman says the local election results have laid down the "battlelines" for the upcoming general election.
"The result now sets up a Westminster poll on 8 June in which independence will be the number one issue," the paper adds.
The Scottish Daily Mail claims it was the Conservatives' best-ever council election result in Scotland, while the SNP "saw its vote plummet compared to recent elections".
However, the Scottish Sun says the surge in support for the Conservatives came at the expense of votes for the Labour party, which "suffered a bruising ... defeat". Despite the Tory comeback, the SNP was still the "runaway winner", it added.
Scotland's "constitutional obsession" sparked the Tories revival, according to the Daily Record. It notes that the "party of Thatcher" even won a council seat in Ravenscraig, "25 years after she sounded the death knell for the Motherwell steelworks".
Meanwhile the Aberdeen edition of The Press and Journal reports that the SNP is poised to take over control of the city council after support for Labour fell.
In Dundee the SNP lost their overall majority, according to The Courier, but the SNP group leader is still likely to run the council, as head of either a minority administration or a coalition.