We study the effect of superradiance in open quantum systems, i.e., the separation of short- and long-living eigenstates when a certain subspace of states in the Hilbert space acquires an increasing decay width. We use several Hamiltonian forms of the initial closed system and generate their coupling to continuum by means of the random matrix theory. We average the results over a large number of statistical realizations of an effective non-Hermitian Hamiltonian and relate robust features of the superradiance process to the distribution of its exceptional points. We show that the superradiance effect is enhanced if the initial system is at the point of quantum criticality.