Lets say your source files are in Server1 and you want to get those files out to Server2, Server3, and Server4.
Your source files are in a share called Source on Server1.
each one of your destination servers has the target directory shared out as Target.
Robocopy \\Server1\Source \\Server2\Destination /MIR /LOG+:Server2.log /NP
Robocopy \\Server1\Source \\Server3\Destination /MIR /LOG+:Server3.log /NP
Robocopy \\Server1\Source \\Server4\Destination /MIR /LOG+:Server4.log /NP
etc
What this script does is it syncs the source folder (and all subdirectories) with the destination folder ( on all subdirectories)
So if you add a file to the source folder the next time the script is run it will add that file to all the destination folders.
If you delete a file to the source folder the next time the script is run it will delete that file from all the destination folders.
So your source folder becomes your master copy.
The /log switch creates a log file in the same directory as your script which records each transaction.
The /NP switch hides the progress bar.
You can run the script manually or schedule it using the WIndows scheduler.