[AT&T, Rogers, Bell, Telus Samsung Galaxy S III] axr0284:
BTW I did not use TWRP simply because most of the help website use CWMRecovery. TWRP is pretty good. I have it running on my kindle fire.

Ok so I finally got it to work. Here are my steps I did:

I have not posted any files or links to them. I don't know how to do it. You can probably search for them.

Note also that these steps can be merged once you are familiar with them.

BTW I also copied some steps directly from some websites <--- Avoid plagiarism here

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TO ROOT AT&T GALAXY S3 SGH-I747

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Initial Setup

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1) Install USB drivers for Samsung AT&T Galaxy S3 SGH-I747 "ATT_I747_GSIII_Samsung_USB_Driver_v1_4_6_0.exe"

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Install CWM recovery.

This is used to backup the phone before making any other changes

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1) Get into the download mode.

a) Hold Down Volume Down, Center Home, and Power buttons together for about 10 seconds.

b) When your phone resets (screen goes off), let go of the Power button but keep holding down the other buttons. Release all buttons once you see a screen that says

Warning!!

A custom OS can cause ....

...

yellow triangle picture.

c) Press volume up

The screen will display

ODIN mode

...

Downloading...

2) Once in Download mode, connect microUSB cable from your AT&T Galaxy S3 SGH-I747 to your computer.

3) When the PC is done installing the USB drivers, Open ODIN 3.07 Program. You should see a blue-highlighted box with a number.

Mine said "0:[COM3]"

4) deselect the "Auto Reboot" option

5) Click on “PDA” then choose the file “CWM-Recovery.tar” (This is CMW-recovery 5.5.0.4) and hit “Start”.

If download was successful, Odin3 will say PASS! in green

----> The following section only applies if you did the ATT/Samsung Over the air (OTA) update.

6)

a) Remove battery

b) Disconnect usb cable

c) Put battery back in

<------

7) Hold Down Volume Up, Center Home, and Power buttons together for about 10 seconds.

8) When the screen appears with the white samsung logo and the blue letters at the top left corner, release all buttons.

This should get you into CWM recovery mode

9) Choose "Backup and restore"

10) Choose "Backup to internal sdcard"

The phone will start the backup of everything on the internal sdcard.

11) After it's done back up choose "reboot system now"

12) After the phone reboots, connect back the usb cable

13) Copy the folder located in clockworkmod\backup\ on the internal sdcard to the computer.

14) Reboot your phone

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ROOT the device and install the super user app

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1) Connect the phone to the computer using the usb cable

2) copy the file “CWM-SuperSU-v0.96.zip” to anywhere on your phone.

3) Perform steps 1 to 8 in section "Install CWM recovery".

4) Once in ClockworkMod Recovery (also known as CWM Recovery), choose “install zip from sdcard”.

5) Next choose “choose zip from sdcard” or “choose zip from internal sdcard”, depending on where you copied the file over to earlier.

6) Choose the file “CWM-SuperSU-v0.96.zip”.

7) Choose “yes”.

CWM should say "Install from sdcard complete" if everything went well

8) Choose "Go Back"

9) Reboot your phone and your AT&T Galaxy S3 SGH-I747 is now fully rooted and with SuperSU app, which is the Superuser app. It should be located in the app drawer

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Prevent system from overwriting CWM

*****

After the OTA update from AT&T/Samsung, the system now overwrites the bootloader with it's own on every reboot. To prevent this two files needs to be modified in the systems folder.

To do this a file explorer will need to be installed such as EX file explorer. Allow it super user access in it's settings

1) copy these two files to your computer and then delete them:

/system/recovery-from-boot.p and /system/etc/install-recovery.sh

2) Perform steps 1 to 8 in section "Install CWM recovery".

3) Reboot your phone

CWM should still be there next time you try recovery

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Update to the latest CWM

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1) Download ROM manager through the app store

2) Make sure you are connected to wifi

3) Open ROM manager and click "Flash ClockWorkmod Recovery

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Installing ROM

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>>>> You need to perform steps in "update to the latest CWM Recovery" before continuing <<<<<

1) Download zip file from the web and store on phone's internal sd card

2) Reboot to recovery

3) Choose "install from zip" and locate your zip file

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Install google apps if not located in ROM

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1) Move "gapps-jb-20120726-signed.zip" to phone and install through recovery.

This is what worked for me at the time I wrote this. Hopefully it will help somebody else.