  The disk mass is among the most important input parameter for every planet
formation model to determine the number and masses of the planets that can
form. We present an ALMA 887micron survey of the disk population around objects
from 2 to 0.03Msun in the nearby 2Myr-old Chamaeleon I star-forming region. We
detect thermal dust emission from 66 out of 93 disks, spatially resolve 34 of
them, and identify two disks with large dust cavities of about 45AU in radius.
Assuming isothermal and optically thin emission, we convert the 887micron flux
densities into dust disk masses, hereafter Mdust. We find that the Mdust-Mstar
relation is steeper than linear with power law indices 1.3-1.9, where the range
reflects two extremes of the possible relation between the average dust
temperature and stellar luminosity. By re-analyzing all millimeter data
available for nearby regions in a self-consistent way, we show that the 1-3
Myr-old regions of Taurus, Lupus, and Chamaeleon I share the same Mdust-Mstar
relation, while the 10Myr-old Upper Sco association has a steeper relation.
Theoretical models of grain growth, drift, and fragmentation reproduce this
trend and suggest that disks are in the fragmentation-limited regime. In this
regime millimeter grains will be located closer in around lower-mass stars, a
prediction that can be tested with deeper and higher spatial resolution ALMA
observations.
