  We investigate the evolution of accretion luminosity $L_{\rm acc}$ and
stellar luminosity ${L_\ast}$ in pre-mainsequence stars. We make the assumption
that when the star appears as a Class II object, the major phase of accretion
is long past, and the accretion disc has entered its asymptotic phase. We use
an approximate stellar evolution scheme for accreting pre-mainsequence stars
based on Hartmann, Cassen & Kenyon, 1997. We show that the observed range of
values $k = L_{\rm acc}/L_\ast$ between 0.01 and 1 can be reproduced if the
values of the disc mass fraction $M_{\rm disc}/M_*$ at the start of the T Tauri
phase lie in the range 0.01 -- 0.2, independent of stellar mass. We also show
that the observed upper bound of $L_{\rm acc} \sim L_\ast$ is a generic feature
of such disc accretion. We conclude that as long as the data uniformly fills
the region between this upper bound and observational detection thresholds,
then the degeneracies between age, mass and accretion history severely limit
the use of this data for constraining possible scalings between disc properties
and stellar mass.
