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For Git & Mercurial TeamCity provides additional build parameters with names of VCS branches known on the moment of build starting. If build took a revision from branch refs/heads/bugfix TeamCity will add configuration parameter with name:
teamcity.build.vcs.branch.<simplified root name>
In addition to this parameter name VCS branch is now shown on build changes page as well in revisions table:
!revisions_table.tag!