[Galaxy S III General] GaryLiao:
I used these exact steps below. They were written by another member a few pages back:

These are the xact steps that I used

1. Used Odin3 3.06, to flash back the China Unicom ROM. Use the instructions on the gfan (bbs.gfan.com/android-4381769-1-1.html) to download I9300ZNLE9.7z and flash the phone. This contains all the required software components (Odin3 3.06, pit, csc, etc). Follow the image posted in the 1st message. Even if you don't understand Chinese, the picture is very clear. This step will re-partition and clear out out everything to get back to the original state.

2. Once the I9300ZNLE9.7z flashing is complete (this must be successful), go through the basic phone setup and then dial *#1234# to confirm the AP, CP, and CSC. This is show the defaut china unicom values I9300ZNALE9, I9300ZNLE9, I9300CHUALE9. Make sure there is none with unknown value!!!!

3. copy CWM-SuperSU-v0.89.zip into the root folder of the external SD-Card

4. Install CWM recovery. Restart the phone in download mode (volume down + home + power on key) and flash "CF-SGS3-CWM-v5.5-v1.2.tar" using Odin3 v3.06

5. Time to Root the phone. Restart the phone in recovery mode (volume up + home + power on key) and install CWM-SuperSU-v0.89.zip from sd-card

6. Restart phone, confirm that SuperSU is installed. If so, then you have rooted the phone! yeah!

7. Dial *#1234#, comfirm that your AP, CP, CSC have the same values china unicom values (I9300ZNALE9, I9300ZNLE9, I9300CHUALE9). if so, great!! you have a rooted phone with no problems right now

8. Copy cwmmanager.apk (i have a file with this name, but forget where i got it from) and Install this application - CWM Manager v3.60 from chain fire. After installation, confirm that you are able to start the application and grant it superuser permission

9. Using CWM Manager v3.60 create a backup to the /mnt/extSdCard (i recommend that you put is on the external SD card!!!) If things go wrong later, this step will be your starting point after a CWM restore

10. Download MobileODINLite-v2.45.apk from xdx-developer forum, copy it into the SD, and install the application. Start up application and give it superuser permission

11. Now it's time to flash the ROM that we really want! Copy "I9300XXALF2_I9300OXAALF2_I9300XXLF2_HOME.tar. md5" to the internal Sd. Open Mobile odin, browse to locate the md5 file, ad then Flash!!! This is flash successfully and restart the phone

12. When the phone starts up, it will start showing some popup error messages.. No problem, just close out the popups and restart the phone in recovery mode (volume up + home + power on key) and do a factory reset / wipe cache. The restart phone

13. when the phone starts up, go through the basic setup. Most important, dial *#1234# to confirm (AP: I9300XXALF2, CP: I9300XXLF2, CSC: I9300OXAALF2) is present. There should not be anything with unknown value!!! If this is what you have, then the hard part is over and you are almost done

14. Now, you need to root the phone again. copy CWM-SuperSU-v0.89.zip into the root folder of the external SD-Card. Restart the phone in recovery mode (volume up + home + power on key) and install CWM-SuperSU-v0.89.zip from sd-card

15. When the phone starts up, dial *#1234# to confirm (AP: I9300XXALF2, CP: I9300XXLF2, CSC: I9300OXAALF2). If so, things are "all good!" and now it's time to create a backup image of you rooted phone with the I9300XXALF2 ROM

16. reinstall - CWM Manager v3.60 from chain fire. After installation, confirm that you are able to start the application and grant it superuser permission

17. Using CWM Manager v3.60 create a new backup to the /mnt/extSdCard (i recommend that you put is on the external SD card!!!) . Once this is done, you are finished and now have a safe way to recover to this point. This is nice to have if you want to experiement with another ROM like cyanogenmod. Who knows!!!

I hope it works for all of you! Thanks to many of you that have provided advise to get this far: Monsier Mona, aZooZa, xda, etc!!