We present a study of accretion in a sample of 45 young, low mass objects in a variety of star forming regions and young associations, about half of which are likely substellar. Based primarily on the presence of broad, asymmetric Halpha emission, we have identified 13 objects (~30% of our sample) which are strong candidates for ongoing accretion. At least 3 of these are substellar. We do not detect significant continuum veiling in most of the accretors with late spectral types (M5-M7). Accretion shock models show that lack of measurable veiling allows us to place an upper limit to the mass accretion rates of <~ 10^{-10} Msun/yr. Using magnetospheric accretion models with appropriate (sub)stellar parameters, we can successfully explain the accretor Halpha emission line profiles, and derive quantitative estimates of accretion rates in the range 10^{-12} < Mdot < 10^{-9} Msun/yr. There is a clear trend of decreasing accretion rate with stellar mass, with mean accretion rates declining by 3-4 orders of magnitude over ~ 1 - 0.05 Msun.
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