How to use MsBuild MsDeployPublish to target local file system?

As per my answer from Using MSBuild, how do I build an MVC4 solution from the command line (applying Web.config transformations in the process) and output to a folder?

msbuild ProjectFile.csproj /p:Configuration=Release ^
                           /p:Platform=AnyCPU ^
                           /t:WebPublish ^
                           /p:WebPublishMethod=FileSystem ^
                           /p:DeleteExistingFiles=True ^
                           /p:publishUrl=c:\output

Or if you are building the solution file:

msbuild Solution.sln /p:Configuration=Release ^ 
                     /p:DeployOnBuild=True ^
                     /p:DeployDefaultTarget=WebPublish ^
                     /p:WebPublishMethod=FileSystem ^
                     /p:DeleteExistingFiles=True ^
                     /p:publishUrl=c:\output

You can also target the project via the solution using the /t:SolutionFolder/Project:Target syntax:

msbuild Solution.sln /t:SolutionFolder/ProjectFile:WebPublish ^
                     /p:Configuration=Release ^ 
                     /p:WebPublishMethod=FileSystem ^
                     /p:DeleteExistingFiles=True ^
                     /p:publishUrl=c:\output