  Some years ago, Cho and Vilenkin, introduced a model which presents
topological solutions, despite not having degenerate vacua as is usually
expected. Here we present a new model with topological defects, connecting
degenerate vacua but which in a certain limit recovers precisely the one
proposed originally by Cho and Vilenkin. In other words, we found a kind of
parent model for the so called vacuumless model. Then the idea is extended to a
model recently introduced by Bazeia et al. Finally, we trace some comments the
case of the Liouville model.
