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The Brownian force model (BFM) is a mean-field model for the local velocitiesduring avalanches in elastic interfaces of internal space dimension $d$, drivenin a random medium. It is exactly solvable via a non-linear differentialequation. We study avalanches following a kick, i.e. a step in the drivingforce. We first recall the calculation of the distributions of the global size(total swept area) and of the local jump size for an arbitrary kick amplitude.We extend this calculation to the joint density of local and global sizeswithin a single avalanche, in the limit of an infinitesimal kick. When theinterface is driven by a single point we find new exponents $\tau_0=5/3$ and$\tau=7/4$, depending on whether the force or the displacement is imposed. Weshow that the extension of a single avalanche along one internal direction(i.e. the total length in $d=1$) is finite and we calculate its distribution,following either a local or a global kick. In all cases it exhibits adivergence $P(\ell) \sim \ell^{-3}$ at small $\ell$. Most of our results aretested in a numerical simulation in dimension $d=1$.

Distribution of joint local and total size and of extension for avalanches in the Brownian force model