  The Time-dependent Hartree-Fock (TDHF) theory is applied to the study of
heavy ion collisions at energies around the Coulomb barrier. The competition
between fusion and nucleon transfer mechanisms is investigated. For
intermediate mass systems such as 16O+208Pb, proton transfer favors fusion by
reducing the Coulomb repulsion. A comparison with sub-barrier transfer
experimental data shows that pairing correlations are playing an important role
in enhancing proton pair transfer. For heavier and more symmetric systems, a
fusion hindrance is observed due to the dominance of the quasi-fission process.
Typical quasi-fission time of few zeptoseconds are obtained. Actinide
collisions are also investigated both within the TDHF approach and with the
Ballian-V\'en\'eroni prescription for fluctuation and correlation of one-body
observables. The possible formation of new heavy neutron-rich nuclei in
actinide collisions is discussed.
