I bought a cheapo MHL adapter from Amazon (around £6). It works well with both the Tablet Z and my HTC One, in fact with HD videos the picture/sound quality is superb. It's just annoying that it needs to be powered from a USB cable. I'll be interested to hear if yours needs external power too.
One nice thing is that when you plug it into the TV, the Tablet Z changes to a media centre mode. A quick stab of the 'Home' button takes you back to the normal UI if you prefer it.