The grapevine may be abuzz with rumors that Samsung is working on the successor of its best-selling Galaxy S3 smartphone, dubbed the Galaxy S4, but it seems that the company has not forgotten about its flagship smartphone for 2012.

Per reports, Samsung has started rolling out the Android 4.1.2 Jelly Bean software update for its Galaxy S3 LTE "GT-I9305."

"Samsung has just started to push Android 4.1.2 Jelly Bean update to the International Samsung Galaxy S III LTE GT-I9305. The Galaxy S III is Samsung's flagship device of the year and is also it's biggest worldwide selling device," stated a SamMobile report.

According to the report, the update from Samsung will be rolled out in phases and may not be available yet for all devices and in all regions.

"You might not be able to update your device to Android 4.1.2 Jelly Bean right away as the update is rolling out in phases. So, it might not yet be available for your country or network provider (If Your device is Carrier branded) but don't worry the update will arrive soon," noted SamMobile.

The Galaxy S3 LTE smartphone can be upgraded either over the air (OTA) or via Samsung Kies software.

The Android 4.1.2 Jelly Bean OS update for the Galaxy S3 LTE from Samsung brings several new features users' way. Most of the enhancements are similar to those for the Galaxy Note 2 and the upgrade brings Multi-Window View and Page Buddy features among other.

Earlier in December, Samsung had started rolling out the Android 4.1.2 update for the Galaxy S3 GT-I9300, beginning with Poland.

Some of the enhancements the new software update brings are the Multi-View Window feature, Page Buddy, new Gallery app (like the Galaxy Note 2), a customizable Notification Panel, disabling of brightness in Notification panel, inputs in Samsung Keyboard (like Swipe), Paper Artis app, Smart Rotation, and Group Cast app for media sharing.