  Calculations of the $^{16}$O$(e,e'pN)$ cross sections to the ground state and
first excited levels of the $^{14}$C and $^{14}$N nuclei are presented.
  The effects of nuclear fragmentation have been obtained in a self-consistent
approach and are accounted for in the determination of the two-nucleon removal
amplitudes.
  The Hilbert space is partitioned in order to compute the contribution of both
long- and short-range effects in a separate way.
  Both the two-proton and the proton-neutron emission cross sections have been
computed within the same models for the reaction mechanism and the contribution
from nuclear structure, with the aim of better comparing the differences
between the two physical processes.
  The $^{16}$O$(e,e'pp)$ reaction is found to be sensitive to short-range
correlations, in agreement with previous results. The $^{16}$O$(e,e'pn)$ cross
section to $1^+$ final states is dominated by the $\Delta$ current and tensor
correlations. For both reactions, the interplay between collective (long-range)
effects and short-range and tensor correlations plays an important role. This
suggests that the selectivity of $(e,e'pN)$ reactions to the final state can be
used to probe correlations also beyond short-range effects.
