  Calculations are presented for the time evolution of $^{240}$Pu from the
proximity of the outer saddle point until the fission fragments are well
separated, using the time-dependent density functional theory extended to
superfluid systems. We have tested three families of nuclear energy density
functionals and found that all functionals exhibit a similar dynamics: the
collective motion is highly dissipative and with little trace of inertial
dynamics, due to the one-body dissipation mechanism alone. This finding
justifies the validity of using the overdamped collective motion approach and
to some extent the main assumptions in statistical models of fission. This
conclusion is robust with respect to the nuclear energy density functional
used. The configurations and interactions left out of the present theory
framework only increase the role of the dissipative couplings. An unexpected
finding is varying the pairing strength within a quite large range has only
minor effects on the dynamics. We find notable differences in the excitation
energy sharing between the fission fragments in the cases of spontaneous and
induced fission. With increasing initial excitation energy of the fissioning
nucleus more excitation energy is deposited in the heavy fragment, in agreement
with experimental data on average neutron multiplicities.
