Printrbot Introduces the Printrbelt

[Feign]

Neat bit of kit - but infinite x not z. Z is height.
Still trying to figure out how that canted extruder can print 6 inches straight up.

Z-axis in relation to the direction of the layers. It has a limited envelope in which it can print any given layer, but an unlimited number of layers it can print.
As for the overhang issue, overhangs on the leading edge of the print need supports going diagonally down to the plate. Supports in general would be going in the direction parallel to the nozzle, not perpendicular to the belt.
The website for the Blackbelt gives a clear explanation for it here, and they show off some counter-intuitive overhang tricks it can do.

Edit: added link