  A grid comb model is a generalization of the well known comb model, and it
consists of $N$ backbones. For $N=1$ the system reduces to the comb model where
subdiffusion takes place with the transport exponent $1/2$. We present an exact
analytical evaluation of the transport exponent of anomalous diffusion for
finite and infinite number of backbones. We show that for an arbitrarily large
but finite number of backbones the transport exponent does not change. Contrary
to that, for an infinite number of backbones, the transport exponent depends on
the fractal dimension of the backbone structure.
