i would like to share a new app with you. It´s called Towelroot. It roots your Device instantly.
Just go to http://towelroot.com and click on the lambda. Install it and click make it rain.
It Works!! No need for Recovery or anything else. Locked Bootloader AND Unlocked Bootloader.
My Tab Z runs the latest 4.4.2 so it works with the latest firmware.
Geohot (creator of towel root) says that it roots nearly every device. So keep on sharing.
Below i have two Screenshots for evidence.