This work aims to derive accretion rates for a sample of 38 HAeBe stars. We apply magnetospheric accretion (MA) shock modelling to reproduce the observed Balmer excesses. We look for possible correlations with the strength of the Halpha, [OI]6300, and Brgamma emission lines. The median mass accretion rate is 2 x 10^-7 Msun yr^-1 in our sample. The model fails to reproduce the large Balmer excesses shown by the four hottest stars (T* > 12000 K). We derive Macc propto M*^5 and Lacc propto L*^1.2 for our sample, with scatter. Empirical calibrations relating the accretion and the Halpha, [OI]6300, and Brgamma luminosities are provided. The slopes in our expressions are slightly shallower than those for lower mass stars, but the difference is within the uncertainties, except for the [OI]6300 line. The Halpha 10% width is uncorrelated with Macc, unlike for the lower mass regime. The mean Halpha width shows higher values as the projected rotational velocities of HAe stars increase, which agrees with MA. The accretion rate variations in the sample are typically lower than 0.5 dex on timescales of days to months, Our data suggest that the changes in the Balmer excess are uncorrelated to the simultaneous changes of the line luminosities. The Balmer excesses and Halpha line widths of HAe stars can be interpreted within the context of MA, which is not the case for several HBes. The steep trend relating Macc and M* can be explained from the mass-age distribution characterizing HAeBe stars. The line luminosities used for low-mass objects are also valid to estimate typical accretion rates for the intermediate-mass regime under similar empirical expressions. However, we suggest that several of these calibrations are driven by the stellar luminosity.
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