My apologies for necro'ing this 3+ Yr dormant thread (& forum for that matter,LOL),BUT ,I just got this tablet a couple weeks ago.
For anyone that's on the latest official stock firmware (US Model TF 300T):
Android 4.2.1,Build NumberJOP40D.US_epad-10.6.1.27.5-20130902
1) Bootloader unlock w/the official ASUS unlocking app works easy enough.
2) Installed unofficial TWRP 2.8.7.2@AREA51 using typical adb commands.
3) I had a lot of trial & error rooting this latest version,though,tried the SuperSU 2.46 stable zip,no-go.
Also tried an old Superuser .zip by ChainsDD,that didn't work either.
Decided to go with the dreaded Kingroot v 4.1 app & it worked,with the intention of using Super Sume PRO to uninstall Kingroot & install SuperSu.
The uninstall of Kingroot worked,but,the SuperSu install failed,sorta:
While I didn't have full Superuser access,the SuperSu app allowed access to its settings,as if I had root.
After several variations of the above method(s),I decided to do a total uninstall of SuperSu & go through the motions of the app "unrooting" & removing all files/etc... related to root.
Thought after a clean slate w/TWRP Installed & no trace of SuperSu/Superuser/Kingroot on the tablet,I'd give the new Systemless SuperSu 2.62.3 zip a try.
Flashed in recovery & BAM,successful root,no downgrading required!
Used Root Explorer & SD Maid PRO to search for any remnants of the Kingroot/Superuser apps/files/etc... & nothing at all!
To those who haven't ever used a device this old & light on power (compared to devices of 2015),a bit of patience is in order:
The operations/installs/flashing are quite a bit slower,at least on stock Jellybean 4.2.1,just be patient & you'll be rewarded w/a rooted device,ready for flashing ROMS/etc....