I just want to quickly document some of the things I did in order to root my new Samsung Galaxy SIII.
When I got it last weekend the system had Android 4.1.1 on it and it immediately started prompting me to update the ROM Over The Air (OTA). I chose to defer this so I could research available ROMS as sometimes newer ROMS can be harder to root. It turns out there was already a process to root even 4.1.2.
Most of the guides for rooting use Odin which is a Windows only app however Cyanogenmod has a process documented that uses heimdall which is a free software implementation of the same protocol that Odin uses that is also cross platform (including Linux). I found the ROM I wanted to update to (a rooted version of the OTA update for 4.1.2) here:
http://forum.xda-developers.com/showthread.php?t=2178482
I then tried to adapt the process to install Cyanogenmod from here:
http://wiki.cyanogenmod.org/w/Install_CM_for_d2vzw
This got me to a point where clockworkmod allowed me to install the ROM from the xda-developers thread above.
However after I rebooted my phone booted to a yellow notification that said it had prohibited software on it and to take the phone to a Verizon store. I think this was because I accidentally skipped step 7 above:
7. Flash bootloader zipfile via recovery:
The other possibility (and I barely understand this) is that there were compatibility differences between the boot files I installed and the one needed/included with the ROM.
No worries, someone else had this problem and it can be fixed by entering download mode and reflashing a stock ROM. I did that using this guide:
http://forum.xda-developers.com/showthread.php?t=1974114
Now, I think technically heimdall can do this but you have to pass a ton of options and specify each file independently whereas with Odin you can specify just the tar.md5 file, so I fired up a Windows system and just used Odin. That got me back. I followed the rest of the instructions in the last thread to end up with Clockwork Mod Recovery, rooted and with an unlocked bootloader. Then, I used clockworkmod to install the original ROM I wanted from thread 2178482 above.
Whew.
Now I have a good starting point.. Time to figure out how to remove all these Verizon apps.