  It is well known that the distributions of hitting times in Markov chains are
quite irregular, unless the limit as time tends to infinity is considered. We
show that nevertheless for a typical finite irreducible Markov chain and for
nondegenerate initial distributions the tails of the distributions of the
hitting times for the states of a Markov chain can be ordered, i.e., they do
not overlap after a certain finite moment of time.
  If one considers instead each state of a Markov chain as a source rather than
a sink then again the states can generically be ordered according to their
efficiency. The mechanisms underlying these two orderings are essentially
different though.
