World\'s simplest task (see below) is not being executed after I publish my web application project. Any idea why?
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Launch MSBuild with detailed verbosity to see why your target is ignored :
msbuild project.csproj /t:Target_to_Launch /v:d
AfterPublish is called after Publish target, but Publish is not the target called when you publish a web application. Publish is the target for publishing ClickOnce application.
You'll have to find the target used when you call Publish in Visual Studio, it could be Package, WebPublish...