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The disk-outflow connection is thought to play a key role in extractingexcess angular momentum from a forming protostar. We present ALMA 0.25" angularresolution observations - in the dust continuum at 1.33 mm and of the molecularline transitions of $^{12}$CO(2-1) and $^{13}$CO(2-1) - of the circumstellardisk and outflow around the T Tauri star HH30, a rare and beautiful example ofa pre-main sequence star exhibiting a flared edge-on disk, an optical jet, anda CO molecular outflow.  The 1.3 mm continuum emission shows a remarkable elongated morphology alongPA=31.2{\deg}+/-0.1{\deg} that has a constant brightness out to a radius ofr=75 au. The emission is marginally resolved in the transverse direction,implying an intrinsic vertical width $\leq$24 au and an inclination to theline-of-sight i$\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$22 auand extends up to 5" (or 700 au) above the disk plane.  We derive a lower limit to the total mass of the CO cavity/outflow of 1.7E-5M$_\odot$. The CO cavity morphology is that of a hollow cone with semi-openingangle ~35{\deg}. The derived kinematics are consistent with gas flowing alongthe conical surface with a constant velocity of 9.3+/-0.7 km/s. We detect smallrotation signatures (Vphi x sin(i) $\in$ [0.1;0.5] km/s) in the same sense asthe underlying circumstellar disk. From these rotation signatures we infer anaverage specific angular momentum of the outflow of 38+/-15 au km/s ataltitudes 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 sightof i=91{\deg}.  The derived morphology and kinematics of the CO cavity are compatible withexpectations from a slow disk wind, originating either throughphoto-evaporation or magneto-centrifugal processes.

The HH30 edge-on T Tauri star A rotating and precessing monopolar outflow scrutinized by ALMA