Easiest way to root & install recovery on the Samsung Galaxy S3 For Verizon. This method has only been used on this phone and this phone only it won't work with T-Mobile, Sprint or AT&T there is other methods for those phones.
DISCLAIMER: As with any rooting tool, there is some chance that something will go wrong. Use of this tool & tutorial video at your own risk, I will not be responsible if you brick your phone in the process.
WARNING: This should be considered a beta! Don't run it if you aren't comfortable with the possibility of having something go wrong and having to re-Odin back to stock or worse. There is some chance this will give you the "custom unlocked" boot screen and change your system status to "Modified". This is not yet confirmed.
Instructions: 1.Install the USB drivers to your PC before
2. Download the root package open and unzip the files to a new folder.
3. On Your Phone Enable installation of third-party apps (Settings then Security then check Unknown sources.
4. On Your Phone Enable USB debugging (Settings then Developer options then check USB debugging)
5. Double-click RootDebugfs.bat and follow the directions on the screen. Your phone will reboot 3 or 4 times during the process; just leave it plugged in. To be safe, don't switch to any other applications while the root process is running.
6. You will know your finished once your back to the main screen on the root script.
If anything goes wrong it's on you!
Credits: * miloj, for the debugfs root method for the Asus TF300T * sparkym3, for his script for rooting the Asus Transformer Prime - this is a modified version of that script * ChainsDD, for Superuser