  A lattice model of critical spanning webs is considered for the finite
cylinder geometry. Due to the presence of cycles, the model is a generalization
of the known spanning tree model which belongs to the class of logarithmic
theories with central charge $c=-2$. We show that in the scaling limit the
universal part of the partition function for closed boundary conditions at both
edges of the cylinder coincides with the character of symplectic fermions with
periodic boundary conditions and for open boundary at one edge and closed at
the other coincides with the character of symplectic fermions with antiperiodic
boundary conditions.
