  Diffusion on a T fractal lattice under the influence of topological biasing
fields is studied by finite size scaling methods. This allows to avoid
proliferation and singularities which would arise in a renormalization group
approach on infinite system as a consequence of logarithmic diffusion. Within
the scheme, logarithmic diffusion is proved on the basis of an analysis of
various temporal scales such as first passage time moments and survival
probability characteristic time. This confirms and puts on firmer basis
previous renormalization group results. A careful study of the asymptotic
occupation probabilities of different kinds of lattice points allows to
elucidate the mechanism of trapping into dangling ends, which is responsible
  of the logarithmic time dependence of average displacement.
