  A realistic microscopically-based quantum approach to the competition between
fusion and quasi-fission in a heavy fusing system is applied to several
reactions leading to $^{256}$No. Fusion and quasi-fission are described in
terms of a diffusion process of nuclear shapes through a dynamical collective
potential energy landscape which is initially diabatic and gradually becomes
adiabatic. The microscopic ingredients of the theory are obtained with a
realistic two-center shell model based on Woods-Saxon potentials. The results
indicate that (i) the diabatic effects play a very important role in the onset
of fusion hindrance for heavy systems, and (ii) very asymmetric reactions
induced by closed shell nuclei seem to be the best suited to synthesize the
heaviest compound nuclei.
