For those of you who want to root your T-Mobile Galaxy S3 SGH-T999, here’s a specific fail-safe noob guide.
Step 1. Hold down Volume Down, Center Home, and Power button together for about 10 seconds until your phone reboots.
Step 2. Let go of only the Power button when your phone resets. You should see a warning screen like below:
Step 3. Press Volume Up to enter ODIN Download Mode then connect a microUSB cable from your T-Mobile Galaxy S3 to your computer.