
I have read multiple success stories with installation of alternate OS's on the T100TA, and followed instructions for doing so to the letter, but the process always grinds to a halt at the same place.
KALI LINUX HOW TO INSTALL FOR ASUS TRANSFORMER T100TAM INSTALL
I have made sure the operating systems I have tried to install are GPT formatted, but this has the same outcome, just the same as regular MBR and plain copying of ISO files directly to the USB. In the boot order list USB media has been set as first. There is no option to disable fast boot in the boot menu, although I have done so through Windows 8.1's battery settings, I have not determined a way to switch to any CSM boot mode, and there is no setting for USB Legacy Mode. The USB is displayed as a UEFI bootable device, which is the only thing the T100TA can boot from, and when it is selected both from the boot menu and the BIOS setup the tablet screen simply 'refreshes' (flashes black for a fraction of a second and tears slightly) and shows no change in status. The main issue from booting on Windows 8.1 tablets is the secure boot mode that has to be turned off via restarting in UEFI mode, which I have done and double checked and triple checked.

The eeepc only has a 4GB hard drive so I can't install a modern distro but I do run them from a USB stick.

I've run live versions of lubuntu and xubuntu on mine. I suspect your Transformer will run linux just fine. I have read that booting other operating systems via USB is theoretically possible on the Asus Transformer book, but I have not been able to get it to work. I have an ASUS eeepc that came with linux installed.
