  In this work, we initially discuss some physical properties of effective
${\rm SU}(N) \to {\rm Z}(N)$ YMH models, emphasizing the important role of
valence gluons. Next, we review how adjoint fields are naturally generated as
an effective description of "adjoint" loops in $4D$. Finally, we discuss the
consequences that can be learnt from this point of view, and briefly comment on
some improvements.
