  We present results from a study of TESS observations of the eclipsing dwarf
nova system Z Cha, covering both an outburst and a superoutburst. We discover
that Z Cha undergoes hysteretic loops in eclipse depth - out-of-eclipse flux
space in both the outburst and the superoutburst. The direction that these
loops are executed in indicates that the disk size increases during an outburst
before the mass transfer rate through the disk increases, placing constraints
on the physics behind the triggering of outbursts and superoutbursts. By
fitting the signature of the superhump period in a flux-phase diagram, we find
the rate at which this period decreases in this system during a superoutburst
for the first time. We find that the superhumps in this source skip
evolutionary stage "A" seen during most dwarf nova superoutbursts, even though
this evolutionary stage has been seen during previous superoutbursts of the
same object. Finally, O-C values of eclipses in our sample are used to
calculate new ephemerides for the system, strengthening the case for a third
body in Z Cha and placing new constraints on its orbit.
