  In order to study rheological properties of gelling systems in dilute
solution, we investigate the viscosity and the normal stresses in the Zimm
model for randomly crosslinked monomers. The distribution of cluster topologies
and sizes is assumed to be given either by Erd\H os-R\'enyi random graphs or
three-dimensional bond percolation. Within this model the critical behaviour of
the viscosity and of the first normal stress coefficient is determined by the
power-law scaling of their averages over clusters of a given size $n$ with $n$.
We investigate these Mark--Houwink like scaling relations numerically and
conclude that the scaling exponents are independent of the hydrodynamic
interaction strength. The numerically determined exponents agree well with
experimental data for branched polymers. However, we show that this traditional
model of polymer physics is not able to yield a critical divergence at the gel
point of the viscosity for a polydisperse dilute solution of gelation clusters.
A generally accepted scaling relation for the Zimm exponent of the viscosity is
thereby disproved.
