  A classical precursor to a full quantum dynamics for causal sets has been
forumlated in terms of a stochastic sequential growth process in which the
elements of the causal set arise in a sort of accretion process. The transition
probabilities of the Markov growth process satisfy certain physical
requirements of causality and general covariance, and the generic solution with
all transition probabilities non-zero has been found. Here we remove the
assumption of non-zero probabilities, define a reasonable extension of the
physical requirements to cover the case of vanishing probabilities, and find
the completely general solution to these physical conditions. The resulting
family of growth processes has an interesting structure reminiscent of an
``infinite tower of turtles'' cosmology.
