Cell motility and tissue morphogenesis depend crucially on the dynamic remodelling of actomyosin
networks. An actomyosin network consists of an actin polymer network connected by crosslinker
proteins and motor protein myosins that generate internal stresses on the network. A recent discovery
shows that for a range of experimental parameters, actomyosin networks contract to clusters
with a power-law size distribution [Alvarado J. et al. (2013) Nature Physics 9 591]. Here, we
argue that actomyosin networks can exhibit robust critical signature without fine-tuning because
the dynamics of the system can be mapped onto a modified version of percolation with trapping
(PT), which is known to show critical behaviour belonging to the static percolation universality
class without the need of fine-tuning of a control parameter. We further employ our PT model to
generate experimentally testable predictions.