[T-Mobile, Samsung Galaxy SIII] mrRobinson:
This is a completely stock ODIN flashable ROM with root injected into the system image.

This is a fairly easy way to get root WITHOUT tripping the flash counter that will void the warranty. If you don't care about tripping the counter then you can get root other ways.

4.3 Image Notes: With 4.3 images, KNOX is removed in order for root to stick. This will flag the Knox counter. Once you flash one of these 4.3 images you now have the latest factory stock bootloader, radio, etc. Flashing a prior bootloader can hard/soft brick your device. Please read and understand what you are doing.

You can get ODIN here

and the drivers for the SGH-T999 so ODIN can detect your phone can be found at Samsung's site. Click on the Manuals & Downloads tab at the bottom and then on Software for the latest driver.

First

download the stock odin tar that has a rooted system image injected into it:

Note: Always check the MD5 sums before using any of these! Thanks :)

MCT: Mobilicity

GLW: Wind

VTR: Videotron

T-Mobile Image

March 2014 - 4.3 JellyBean

- New!

Note: This is based off of the stock image TMO T999UVUENC2

Do not flash a prior release after flashing this, it has been reported to cause bricks, read the thread for more information.

Perm Mirror: Download - root66_TMO_T999UVUENC2.7z

November 2013 - 4.3 JellyBean

Note: This is based off of the stock image TMO T999UVUEMJC

Do not flash a prior release after flashing this, it has been reported to cause bricks, read the thread for more information.

Perm Mirror: Download - root66_TMO_T999UVUEMJC_2.7z

April 2013 - 4.1.2 JellyBean

Note: This is based off of the stock image TMO T999UVDMD5

Perm Mirror: Download - root66_TMO_T999UVDMD5.7z

January 2013 - 4.1.1 JellyBean

Note: This is based off of the stock image TMO T999UVDLJC

Perm Mirror: Download - root66_TMO_T999UVDLJC.7z

Note: This is based off of the stock image TMO T999UVDLJA (October 2012 - 4.1.1 Jelly Bean

Perm Mirror: Download - root66_TMO_T999UVDLJA.7z

T-Mobile LTE Image

March 2014 - 4.3 JellyBean

- New!

Note: This is based off of the stock image TMO T999LUVUBNC1

Download :: Download - root66_TMO-L_T999LUVUBNC1.7z

December 2013 - 4.3 JellyBean

Note: This is based off of the stock image TMO T999LUVUBMK4

Download :: Download - root66_TMO-L_T999LUVUBMK4.7z

WIND Image

December 2013 - 4.3 JellyBean

Note: This is based off of the stock image GLW T999VVLUEMK5

Download :: Download - root66_GLW_T999VVLUEMK5.7z

June 2013 - 4.1.2 JellyBean

Note: This is based off of the stock image GLW T999VVLDMF2

Perm Mirror: Download - root66_GLW_T999VVLDMF2.7z

December 2012 - 4.1.1 JellyBean

Note: This is based off of the stock image GLW T999VVLDLL1

Perm Mirror: Download - root66_GLW_T999VVLDLL1.7z

Mobilicity Image

December 2013 - 4.3 JellyBean

Note: This is based off of the stock image MCT T999VVLUEMK5

Download :: Download - root66_MCT_T999VVLUEMK5.7z

June 2013 - 4.1.2 JellyBean

Note: This is based off of the stock image MCT T999VVLDMF2

Perm Mirror: Download - root66_MCT_T999VVLDMF2.7z

December 2012 - 4.1.1 JellyBean

Note: This is based off of the stock image MCT T999VVLDLL1

Perm Mirror: Download - root66_MCT_T999VVLDLL1.7z

Videotron Image

December 2013 - 4.3 JellyBean

Note: This is based off of the stock image VTR T999VVLUEMK5

Download :: Download - root66_VTR_T999VVLUEMK5.7z

June 2013 - 4.1.2 JellyBean

Note: This is based off of the stock image VTR T999VVLDMF2

Perm Mirror: Download - root66_VTR_T999VVLDMF2.7z

December 2012 - 4.1.1 JellyBean

Note: This is based off of the stock image VTR T999VVLDLL1

Perm Mirror: Download - root66_VTR_T999VVLDLL1.7z

Second

,

Extract the root66 tar file from the .7z file you downloaded.

Put phone into download mode [ with phone off, hold vol. down + home + power ], connect to computer and open Odin.

once in odin click the PDA field and select the root66 tar you downloaded.

Leave Auto Reboot and F. Reset Time checked.

click start and

when done let phone reboot.

If you have issues flashing with Odin please ensure you are using the microusb cable that came with the phone, users have had issues using other cables.

If you just want a stock, rooted phone with no custom recovery, no plans to flash custom roms, etc. then you can stop HERE.

If you are coming from a different rom base (non-stock) you will want to factory wipe/reset in recovery after flashing this.

OTA Updates:

Stock Recovery:

Once rooted with above method, if you receive a notification for an OTA update, it has been verified you can use OTA RootKeeper to retain root through the update process.

Non-Stock Recovery:

If you have loaded a non-stock recovery (per below) you can simply use it to flash the OTA update flashable zip I've created. This is the stock OTA just modified to be flashable in CWM and TWRP and not lose root in the process. As such it still does all the checks so if you have deviated from the rooted stock image above by modifying system files this will fail.

Download: OTA Update UVALJ4 to UVDLJA

Download: OTA Update UVDLJA to UVDLJC

Third

, (optional)

Note: On Jelly Bean releases it is possible and I'd say probable based on my experience with the Note II that loading a non-stock recovery will trip the counter no matter how you install it.

If you want to get clockworkmod recovery loaded so you can flash whatever you want, nandroid, etc then continue on....

Once rebooted you can essentially follow this thread to load the clockworkmod recovery. As long as you flash the recovery using the dd method with adb (or use terminal emulator from the play store) then you will NOT trip the flash counter. If you use ODIN to flash a custom recovery you will trip the counter.

Third

, alternate if unfamiliar with adb commands and uncomfortable using any command line

Decide if you want to use TWRP or CWM.

If you would like to install ClockworkMod recovery then grab Rom Manager from the Play store and in the menu select to install ClockworkMod Recovery.

If you would like to install TeamWin Recovery Project then grab GooManager from the Play store and select the option to "Install OpenRecovery Script".

De-Bloater

If you've made it this far with a stock, rooted phone with cwm and you don't want to flash a custom rom (which will do its own de-bloating) you can check out my Aroma installer based De-bloater to easily get rid of bloat system apps you no longer want to see. Simply flash in CWM like anything else and you will be presented with a menu system to choose what to remove. If you are unsure it is safe to pick Recommended and still get a decent de-bloat.​

[Note: Flashing this with ODIN will not wipe /sdcard or /data. Keep that in mind depending on your usage.]

Bonus Downloads

Odin Flashable Stock TMO UVDMD5 Recovery - This is an Odin Flashable STOCK Recovery for TMO from UVDMD5 release - TMO_recovery_T999UVDMD5.tar.md5

Odin Flashable TWRP Recovery - openrecovery-twrp-2.3.1.0-d2tmo.tar.md5

Thanks

To get the injected root system image I followed pieces of

http://xdaforums.com/showpost.php?p=27801304&postcount=1

http://xdaforums.com/showpost.php?p=22798858&postcount=32

so thanks to those guys. Neither of those worked out of the box needed a bit of tweaking.