  I present a systematic analysis of formation of the universal annihilation
catastrophe which develops in an open system, where species $A$ and $B$ diffuse
from the bulk of restricted medium and die on its surface (desorb) by the
reaction $A + B \to 0$. This phenomenon arises in the diffusion-controlled
limit as a result of self-organizing explosive growth (drop) of the surface
concentrations of, respectively, slow and fast particles ({\it concentration
explosion}) and manifests itself in the form of an abrupt singular jump of the
desorption flux relaxation rate. As striking results I find the dependences of
time and amplitude of the catastrophe on the initial particle number, and
answer the basic questions of when and how universality is achieved.
