TeamCity builds then copies to each web tier via a powershell script. The steps for each server are:
TeamCity is our main continuous integration server. It starts creating builds and running tests based on commits that we make in our hosted bitbucket repositories. From there, we have a set of configuraitons that can deploy the built and tested artifacts (web app, batches, db, etc...) to a stage or production server. We still release manually, but we release often, and TeamCity has nice features to help us roll back when things don't work out as planned.