Seif-organised criticality (SOC) has been proposed as a potentially powerfu
l unifying paradigm for interpreting non-diffusive avalanche-type transport
in laboratory, space and astrophysical plasmas. After reviewing the most p
romising astrophysical sites where SOC might be observable, we consider the
theoretical arguments for supposing that SOC can occur in accretion discs.
Perhaps the most rigorous evidence is provided by numerical modelling of e
nergy dissipation due to magnetohydrodynamic turbulence in accretion discs
by G. Geertsema & A. Achterberg (Astron. Astrophys. 255, 427 (1992)); we in
vestigate how "sandpile"-type dynamics arise in this model. It is concluded
that the potential sites for SOC in accretion systems are numerous and obs
ervationally accessible, and that theoretical support for the possible occu
rrence of SOC can be derived from first principles.