  The stability and/or instability of the deformed and superdeformed nuclei,
$^{133-137}_{60}$Nd, $^{144-158}_{64}$Gd, $^{176-194}_{80}$Hg, and
$^{192-198}_{82}$Pb parents, coming from three regions of different
superdeformations, are studied with respect to the $\alpha$ and heavy cluster
decays. The $\alpha$-decay studies also include the heavier $^{199-210}$Pb
nuclei, for reasons of spherical magic shells at Z=82 and N=126. The
calculations are made by using the preformed cluster-decay model, and the
obtained $\alpha$-decay half-lives are compared with the available experimental
data. Having met with a very good success for the comparisons of $\alpha$-decay
half-lives and in giving the associated known magic or sub-magic closed shell
structures of both the parent nuclei and daughter products, the interplay of
closed shell effects in the cluster-decay calculations is investigated. The
cluster-decay calculations also give the closed shell effects of known
spherical magicities, both for the parent and daughter nuclei, and further
predict new (deformed) closed shells at Z=72-74 and N=96-104 due to both the
stability and instability of Hg and Pb parents against cluster decays.
Specifically, a new deformed daughter radioactivity is predicted for various
cluster decays of $^{186-190}$Hg and $^{194,195}$Pb parents with the best
possible measurable cases identified as the $^8$Be and $^{12}$C decays of
$^{176,177}$Hg and/or $^{192}$Pb parents. The predicted decay half-lives are
within the measurable limits of the present experimental methods. The
interesting point to note is that the parents with measurable cluster decay
rates are normal deformed nuclei at the transition between normal and
super-deformation.
