T-Mobile now has a post up about the update here: http://support.t-mobile.com/docs/DOC-4446
Understanding the Update
Beginning January 31, the Samsung Galaxy S III will have an optional software update to Android version 4.1.1/ Baseband version T999UVDLJC via Over The Air (OTA) and Samsung Kies. This update provides security enhancements and improved user experience.
You can update in two ways:
Over the air (OTA) update to T999UVDLJC: OTA push update is available as of 1/31/2013. Please wait for the notification to update. The OTA will continue to be delivered until Marth 8. The update is also available for manual update using Kies.
Manual download to T999UVDLJC: If you did not want to update via OTA, you can update via Samsung Kies. Ensure you are on the latest version of Kies prior to attempting the update. See http://www.samsung.com/us/kies/ to confirm the version.
Current Baseband Version Update Status
This software version is current. Your device software is up to date.
The update is still being sent to customers via OTA. You must wait to receive the OTA.
You can manually update to Android version 4.1.1/ Baseband version T999UVDLJC. See above for steps to manually update via Kies.
You can manually update to Android version 4.1.1/ Baseband version T999UVLJA. See above for steps to manually update via Kies.
T-Mobile and Samsung will not send you a software update.
Devices with non-T-Mobile software versions are out of warranty and do not receive updates.
See also: Check the Software version.
Android version 4.1.1/Baseband version T999UVDLJC - Current version
Android version 4.1.1/Software version T999UVDLJC
OTA and Samsung Kies update available 1/31/2013
Improved user experience
Device software is not rooted
50% battery life
Latest version of Kies software downloaded on PC or MAC
File size of update is 4 MB
Android version 4.1.1/Baseband version T999UVDLJA - Approved 11/14/2012
Android version 4.0.4/Baseband version T999UVLJ4 - Approved 10/17/2012
Android version 4.0.4/Baseband version T999UVLH2 - Approved 8/16/2012
Android version 4.0.4/Baseband version T999UVLG1/T999UVLEM - Original software 6/21/2012