  In this Letter we present a theoretical scenario to explain the steep
correlation between disk accretion rates and stellar masses observed in
pre-main sequence stars. We show that the correlations and spread observed in
the two best studied regions, rho-Ophiuchus and Taurus, can be reproduced by a
simple model of single star formation from a rotating collapsing core and the
viscous evolution of the circumstellar disk. In this model, the rate of
rotation of the parent core sets the value of the `centrifugal radius' within
which the infalling matter is loaded onto the surface of the disk. As a
consequence, the disk accretion rate measured long after the dispersal of the
parental core bears the imprint of the initial conditions of star formation.
The observed trend results naturally if, at the onset of the collapse, cores of
all masses rotate with the same distribution of angular velocities, measured in
units of the break-up rotation rate.
