  The disk-outflow connection is thought to play a key role in extracting
excess angular momentum from a forming protostar. We present ALMA 0.25" angular
resolution observations - in the dust continuum at 1.33 mm and of the molecular
line transitions of $^{12}$CO(2-1) and $^{13}$CO(2-1) - of the circumstellar
disk and outflow around the T Tauri star HH30, a rare and beautiful example of
a pre-main sequence star exhibiting a flared edge-on disk, an optical jet, and
a CO molecular outflow.
  The 1.3 mm continuum emission shows a remarkable elongated morphology along
PA=31.2{\deg}+/-0.1{\deg} that has a constant brightness out to a radius of
r=75 au. The emission is marginally resolved in the transverse direction,
implying an intrinsic vertical width $\leq$24 au and an inclination to the
line-of-sight i$\geq$84.8{\deg}. The monopolar outflow, detected in $^{12}$CO,
arises from the north-eastern face of the disk from a disk radius r$\leq$22 au
and extends up to 5" (or 700 au) above the disk plane.
  We derive a lower limit to the total mass of the CO cavity/outflow of 1.7E-5
M$_\odot$. The CO cavity morphology is that of a hollow cone with semi-opening
angle ~35{\deg}. The derived kinematics are consistent with gas flowing along
the conical surface with a constant velocity of 9.3+/-0.7 km/s. We detect small
rotation signatures (Vphi x sin(i) $\in$ [0.1;0.5] km/s) in the same sense as
the underlying circumstellar disk. From these rotation signatures we infer an
average specific angular momentum of the outflow of 38+/-15 au km/s at
altitudes z<250 au. We also report the detection of small amplitude wiggling
(1.2{\deg}) of the CO axis around an average inclination to the line of sight
of i=91{\deg}.
  The derived morphology and kinematics of the CO cavity are compatible with
expectations from a slow disk wind, originating either through
photo-evaporation or magneto-centrifugal processes.
