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.
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