The Samsung Galaxy S III for Verizon is in line for an Android 4.1 Jelly Bean and so far we have seen a few leaked builds appear. Today however a report suggests that the latest K3 build with Android 4.1.1 will be the final version which will be sent over-the-air Verizon customers later this week.
The update will be around 62 MB in size and your device and your device cannot be rooted if you want to get the automatic update. You can always get rooted after receiving the update on your device.
If you don't want to wait for the update to be released for your device, you can get leaked ROM right now and install it on your GSIII using ClockWorkMod Recovery. Your device will have to have its bootloader unlocked and be rooted in order to install the update manually and you can find a guide for that here.
Meanwhile Verizon’s support documents reflect the new features and improvements which will be available for the Samsung Galaxy S III
[SOURCE] XDA Developers | Verizon Wireless
[UPDATE] Verizon has currently removed the K3 update documents from their site. We recon it will be back online when the update is ready for release.