Google has released an Android Jelly Bean 4.1.2 XXEMB5 firmware update and owners of the Samsung Galaxy S3 with an I9300 model number (factory unlocked) can get the update now through Samsung KIES.
Naturally, the first thing you'll want to do after flashing your device is to root it, and this step-by-step guide will explain exactly how to do just that.
Preparations
One does not simply root an Android.
You'll need to download CF-Auto-Root. The package contains SuperSu v.0.93, ClockworkMod (CWM) recovery v5.5 and CWM Manager v3.60.
You'll also need Odin v.185 to install Jelly Bean.
After downloading and unpacking the archives, ensure that your USB Drivers for Samsung Galaxy S3 are current and BACKUP YOUR DEVICE.
Then make sure the battery is charged to at least 80 percent before proceeding.
Step 1: Turn off the phone and enter Download mode. You do that by pressing and holding the Volume Down, Home and Power buttons together until the construction robot comes up and a triangle appears on the screen. When that happens, press the Power button, and you're in download mode.
Step 2: Run Odin.
Step 3: Connect your phone to the computer via USB. If the connection is successful, one of the ID:COM boxes will turn yellow. This step takes some time, so be patient.
Step 4: In Odin, click on PDA and select the CF-Auto-Root-SGS3-v6.4.tar file.
Step 5: Check off Auto Reboot and F.Reset Time in Odin.
Step 6: Click start. The installation process will take a few minutes to complete. Do nothing until it's done.
When the installation is finished, your phone will automatically restart. You can unplug the USB cable once the Home screen appears.
Congratulations, your Samsung Galaxy S3 I93000 running Android 4.1.2 XXEMB5 Jelly Bean is now rooted. You can verify with the Root Checker tool.