  We consider the genealogy tree for a critical branching process conditioned
on non-extinction. We enumerate vertices in each generation of the tree so that
for each two generations one can define a monotone map describing the
ancestor--descendant relation between their vertices. We show that under
appropriate rescaling this family of monotone maps converges in distribution in
a special topology to a limiting flow of discontinuous monotone maps which can
be seen as a continuum tree. This flow is a solution of an SPDE with respect to
a Brownian sheet.
