Are you sick of waiting for Samsung to release the latest and greatest Android os 4.1.1 jellybean? Well I am and that exactly why I installed CyanogenMod 10 on my Galaxy s3 sgh-t999 T-mobile variant. Following this guide WILL void your warranty. I can confirm that this works on the T-mobile Samsung Galaxy s3 and should work on the other USA carriers but have not tried it. You are following this guide at your own risk androidnerds.net can not and will not be held responsible if you damage/brick your phone. OK lets do this.
First make sure your phone is rooted YOU MUST HAVE CLOCKWORK MOD RECOVERY INSTALLED there are plenty of guides online.
Next make a backup of all your data you can use titanium backup or others I use Gcloud from google play.
Keep both files as a zip file and copy them to the root of your external sd card NOT your internal memory.
Boot your device into clockwork mod recovery by turning off your device Then hold the power, home and volume up buttons together until the screen flashes and let go of the buttons. At the top of the screen it
will say clockworkmod recovery if it does not say that DO NOT PROCEED Something went wrong and you may need to flash clockworkmod recovery again.
Once your device is properly in clockworkmod recovery go to erase data and then confirm the action.
Next go to wipe cached partition and confirm that action.
Now that that is all done go back to main screen and click
install zip from sd. Choose the cm-10-20121001-NIGHTLY-d2tmo file and wait for that to complete
Next go back to main screen and choose install zip form sd again but this time pick the gappsSigned.zip file ( This installs google play, gmail, and some other google apps)
Once that is done go back to main screen and chose reboot system now.
Congratulations you have just installed CyanogenMod 10 on your Samsung Galaxy s3. Just go through the start up menu and enter all your details and you are now running Android 4.1.1 Jellybean with out Touchwiz overlay.
T-mobile’s WiFi calling feature is not built into this ROM so if you need that feature don’t install this ROM.
My first impressions of this rom where Wow the speed the overall smoothness of the ui is amazing.