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The dependence of the mass accretion rate on the stellar properties is a keyconstraint for star formation and disk evolution studies. Here we present astudy of a sample of stars in the Chamaeleon I star forming region carried outusing the VLT/X-Shooter spectrograph. The sample is nearly complete down toM~0.1Msun for the young stars still harboring a disk in this region. We derivethe stellar and accretion parameters using a self-consistent method to fit thebroad-band flux-calibrated medium resolution spectrum. The correlation betweenthe accretion luminosity to the stellar luminosity, and of the mass accretionrate to the stellar mass in the logarithmic plane yields slopes of 1.9 and 2.3,respectively. These slopes and the accretion rates are consistent with previousresults in various star forming regions and with different theoreticalframeworks. However, we find that a broken power-law fit, with a steeper slopefor stellar luminosity smaller than ~0.45 Lsun and for stellar masses smallerthan ~ 0.3 Msun, is slightly preferred according to different statisticaltests, but the single power-law model is not excluded. The steeper relation forlower mass stars can be interpreted as a faster evolution in the past foraccretion in disks around these objects, or as different accretion regimes indifferent stellar mass ranges. Finally, we find two regions on the massaccretion versus stellar mass plane empty of objects. One at high massaccretion rates and low stellar masses, which is related to the steeperdependence of the two parameters we derived. The second one is just above theobservational limits imposed by chromospheric emission. This empty region islocated at M~0.3-0.4Msun, typical masses where photoevaporation is known to beeffective, and at mass accretion rates ~10^-10 Msun/yr, a value compatible withthe one expected for photoevaporation to rapidly dissipate the inner disk.

X-Shooter study of accretion in Chamaeleon I: II. A steeper increase of accretion with stellar mass for very low mass stars?