  We revisit the problem of deriving the mean-field values of avalanche
critical exponents in systems with absorbing states. These are well-known to
coincide with those of an un-biased branching process. Here, we show that for
at least 4 different universality classes (directed percolation, dynamical
percolation, the voter model or compact directed percolation class, and the
Manna class of stochastic sandpiles) this common result can be obtained by
mapping the corresponding Langevin equations describing each of these classes
into a random walker confined close to the origin by a logarithmic potential.
Many of the results derived here appear in the literature as independently
derived for individual universality classes or for the branching process.
However, the emergence of non-universal continuously-varying exponent values
--which, as shown here, stems fro the presence of small external driving, that
might induce avalanche merging-- has not been noticed (or emphasized) in the
past. We believe that a simple an unified perspective as the one presented here
can (i) help to clarify the overall picture, (ii) underline the
super-universality of the behavior as well as the dependence on external
driving, and (iii) help avoiding the common existing confusion between
un-biased branching processes (equivalent to a random walker in a balanced
logarithmic potential) and standard (un-confined) random walkers.
