In the Tek 0067, there was a quick mention of the Galaxy SIII being rooted with a custom Nexus Rom. Has anyone got any more information on this (how-to, where to download, etc?) I've been looking to ditch TouchWiz for a while now but I'll be honest, I'm a Android phone noob.
Head over to the XDA-Developers forum where you'll find a section dedicated to the Galaxy S3. Look for the current root method and how to unlock your bootloader. Once you've done that it's as simple as finding a custom ROM that you want. I'd recommend starting with Cyanogen Mod. It's mostly stock android though it does have a few tweaks and features.
Well, rooting and changing ROMs on Samsung is really easy. Jost google it.
As for which ROM to install I recommend P.A.C. It's basically a compilation of features from major branches of custom roms. I'm not sure how it's on S3 but on my S2 it's the most stable ROM I used. You may be overwhelmed by the amount of settings and features at first but I think you'll most of them useful eventually.
I agree with rballen. CyanogenMod 10.1 is just about the most stable custom AOSP out there and will give you the pure android experience (4.2.2). I'm running CM10.1 on HTC sensation and it's really smooth.
Here is cyanogen mod download site http://get.cm/
GS3 is d2 and my GS3 is sprint so my phone is d2spr. Make sure you choose the right phone model or you will have a useless paper weight. Also make sure to download the gapps (google apps) or you will not be able to download from the google play store. Here is a link to the gapps http://goo.im/gapps
You should mention it's very, very, VERY important you're on the forum FOR YOUR CARRIER. Not all phones are equal, and sometimes using another carriers method may get you a bricked (well, soft brick) phone.