  The time evolution of the dependence of the mass accretion rate with the
stellar mass and the disk mass represents a fundamental way to understand the
evolution of protoplanetary disks and the formation of planets. In this work,
we present observations with X-Shooter of 26 Class II very low-mass stars and
brown dwarfs in the Ophiuchus, Cha-I, and Upper Scorpius star-forming regions
(SFRs). These new observations extend down to SpT M9 ($\sim$0.02 $M_\odot$) the
measurement of the mass accretion rate in Ophiuchus and Cha-I and add 11
very-low-mass stars to the sample of objects studied with broadband
spectroscopy in Upper Scorpius. We obtained their SpT, extinction and physical
parameters, and we used the intensity of various emission lines to derive their
accretion luminosity and mass accretion rates. Combining these new observations
with data from the literature, we compare relations between accretion and
stellar and disk properties of four different SFRs with different ages:
Ophiuchus (1 Myr), Lupus (2 Myr), Cha-I (3 Myr), and Upper Scorpius (5-12 Myr).
We find the slopes of the $L_*-L\mathrm{_{acc}}$ and
$M_*-\dot{M}\mathrm{_{acc}}$ relationships to steepen between Ophiuchus, Lupus,
and Cha-I and that both relationships may be better described with a single
power law. We also find the relationship between the disk mass and the mass
accretion rate of the stellar population to steepen with time down to the age
of Upper Scorpius. Overall, we observe hints of a faster evolution into low
accretion rates of low-mass stars and brown dwarfs. We also find that brown
dwarfs present higher $M\mathrm{_{disk}}/\dot{M}\mathrm{_{acc}}$ ratios (i.e.,
longer accretion depletion timescales) than stars in Ophiuchus, Lupus, and
Cha-I. This apparently contradictory result may imply that the evolution of
protoplanetary disks around brown dwarfs is different from what is seen in the
stellar regime.
