Journal of Statistical Physics, Vol. 55, Nos. 5/6, 1989. p. 1053-1064.
Systems with an infinite variety of types of splitting particles are investigated. It is shown that if there is a stationary source of particles but no sink, a steady state with finite density of each species is nevertheless possible due to the infinite number of degrees of freedom. It is demonstrated that the limiting (steady) state
is independent of the initial state of the system. Typical features of the steady state, which do not depend on the particle splitting law, are shown.