Rooting US Galaxy S III variants isn’t much of a big thing to do except the Verizon one. The US Galaxy S III is rooted using Odin that results in two things. One that the flash counter ticks off and the other is a yellow triangle that users have to deal with everyday. But now there’s a root method for T-Mobile/Wind/Moblicity Galaxy S III that avoids both, the irritating yellow triangle and ticking the flash counter.
So if the standard method does move up the flash counter and shows the irritating yellow triangle then obviously something more than that is required in order to avoid those two things. But what’s more interesting is that this method still uses the Odin but instead of the using the whole file, only a single file from a rooted stock image called root66 has been used. So users have to download the complete half a GB system image file in order to get that specific root66 file. Though the rest of the process is pretty simple. You just need to download the rooted system image and extract ‘root66.tar’ file and flash it over Odin with Auto Restart and F Time Reset option ticked. This is the simplest of the methods to root your US Galaxy S III. The device will be rooted then and you will no longer see that yellow triangle. While for installing a custom recovery and flashing ROM there’s a thread provided from the developer to make sure that after rooting users don’t get tripped their flash counter. So for download links and more information on the root and installing the custom recovery, check out this thread.
Source: XDA Developers