  In this article, we study the existence of an absorbing-state phase
transition of an Abelian process that generalises the Activated Random Walk
(ARW). Given a vertex transitive $G=(V,E)$, we associate to each site $x \in V$
a capacity $w_x \ge 0$, which describes how many inactive particles $x$ can
hold, where $\{w_x\}_{x \in V}$ is a collection of i.i.d random variables. When
$G$ is an amenable graph, we prove that if $\mathbb E[w_x]<\infty$, the model
goes through an absorbing state phase transition and if $\mathbb
E[w_x]=\infty$, the model fixates for all $\lambda>0$. Moreover, in the former
case, we provide bounds for the critical density that match the ones available
in the classical Activated Random Walk.
