  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.
