  An imitation of 2d field theory is formulated by means of a model on the
hierarhic tree (with branching number close to one) with the same potential and
the free correlators identical to 2d correlators ones.
  Such a model carries on some features of the original model for certain scale
invariant theories. For the case of 2d conformal models it is possible to
derive exact results. The renormalization group equation for the free energy is
noiseless KPZ equation with additional linear term.
