These are the instructions to root Samsung Galaxy S3 Mini GT-I8190 using pre-rooted Stock Rom (android 4.1.2 base-XXAMG1).
Requirements: Your Samsung Galaxy S3 Mini GT-I8190 should have at least 30-40 percent of battery to perform the rooting process.
Step 1: Download and Install Samsung USB Driver on your computer. If Samsung USB Driver already installed on your computer then Skip this Step.
Step 2: Download and extract the root files on your computer. After extracting you will be able to see the following files:
Step 3: Power Off your Samsung Galaxy S3 Mini GT-I8190.
Step 4: Now, you have to enter into Download Mode on your phone by Pressing Volume Down Key, Home Button and Power key at same time for 5-8 seconds until you entered to the download mode.
Step 5: In the Download mode you will be able to see a Warning Triangle Sign. In this situation you have to press the Volume up key to continue.
Step 6: Now, Open Odin3 (found in the extracted folder, that you have downloaded in the Step#2) on your computer. Then connect your phone to the computer.
Step 7: Once you have connected the phone to the computer, Oden will automatically recognize the device and show “Added” message at the lower-left panel.
Step 8: Once your device detected by Odin, click on the PDA button and select the I8190OXXAMG1 PRE-ROOTED.tar file (you have extracted this file in step#2).
Step 9: Now, click on the Start button in odin to begin the Flashing. Once flash process is completed your phone will restart automatically.
Step 10: Once you see, the Green Pass Message then remove the USB cable from the device (during this process, your device will restart automatically).
Step 11: Now your Samsung Galaxy S3 Mini GT-I8190 is Rooted. To check whether your phone is rooted correctly, open Applications Menu, there you will be able to see a new app installed, called SuperSU. If this app exist then it means you have successfully rooted your device.
Optional: You can also verify the root status of your device by using the Root Checker Application.
[*] Data Loss Process: Flashing Pre-Rooted Stock ROM is always a data loss procedure. So, always take backup of your personal data before flashing the Stock ROM.
[*] Warranty Void: Your Samsung Galaxy S3 Mini GT-I8190 Warranty may be Void after following the above tutorial.
[*] How to Unroot? To unroot Open SuperSU > Settings > Full Unroot.
[*] Samsung Stock Firmware: If you are looking for the original firmware for your device then head over to Download Samsung Stock Firmware for all devices page.
[*] Samsung USB Driver: If you are looking for the original USB Driver for your device then head over to Download Samsung USB Driver for all devices page.
[*] Credits: The Pre-Rooted firmware used in this tutorial is made available by Avicohh (xda developer). Very thanks for the firmware, without it the above tutorial was not possible.