  We consider the asymmetric random average process (ARAP) with continuous mass
variables and parallel discrete time dynamics studied recently by Krug/Garcia
and Rajesh/Majumdar [both Jrl. Stat. Phys. 99 (2000)]. The model is defined by
an arbitrary state-independent fraction density function $\phi(r)$ with support
on the unit interval. We examine the exactness of mean-field steady-state mass
distributions in dependence of $\phi$ and identify as a conjecture based on
high order calculations the class $\mathcal{M}$ of density functions yielding
product measure solutions. Additionally the exact form of the associated mass
distributions P(m) is derived. Using these results we show examplary the
exactness of the mean-field ansatz for monomial fraction densities
$\phi(r)=(n-1) r^{n-2}$ with $n \geq 2$. For verification we calculate the mass
distributions P(m) explicitly and prove directly that product measure holds.
Furthermore we show that even in cases where the steady state is not given by a
product measure very accurate approximants can be found in the class
$\mathcal{M}$.
