  The Solar System gas giants are each surrounded by many moons, with at least
50 prograde satellites thought to have formed from circumplanetary material.
Just like the Sun is not the only star surrounded by planets, extrasolar gas
giants are likely surrounded by satellite systems. Here, we report on ALMA
observations of four <40 Myr old stars with directly-imaged companions: PZ Tel,
AB Pic, 51 Eri, and $\kappa$ And. Continuum emission at 1.3 mm is undetected
for any of the systems. Since these are directly-imaged companions, there is
knowledge of their temperatures, masses and locations. These allow for upper
limits on the amount of circumplanetary dust to be derived from detailed
radiative transfer models. These protolunar disc models consider two disc
sizes: 0.4 and 0.04 times the exoplanet's Hill radius. The former is
representative of hydrodynamic simulations of circumplanetary discs while the
latter a case with significant radial drift of solids. The more compact case is
also motivated by the semi-major axis of Callisto, enclosing Jupiter's Galilean
satellites. All upper limits fall below the expected amount of dust required to
explain regular satellite systems ($10^{-4}$ times the mass of their central
planet). Upper limits are compared with viscous evolution and debris disc
models. Our analysis suggests that the non detections can be interpreted as
evidence of dust growth beyond metre sizes to form moonetesimals in timescales
<10 Myr. This sample increases by 50% the number of ALMA non-detections of
young companions available in the literature.
