  We construct diffusions with values in the nonnegative orthant, normal
reflection along each of the axes, and two pairs of local drift/variance
characteristics assigned according to rank; one of the variances is allowed to
vanish, but not both. The construction involves solving a system of coupled
Skorokhod reflection equations, then ``unfolding'' the Skorokhod reflection of
a suitable semimartingale in the manner of Prokaj (Statist. Probab. Lett. 79
(2009) 534-536). Questions of pathwise uniqueness and strength are also
addressed, for systems of stochastic differential equations with reflection
that realize these diffusions. When the variance of the laggard is at least as
large as that of the leader, it is shown that the corner of the quadrant is
never visited.
