It is shown that the existence of various strange superatomic Boolean algebras is consistent with ZFC set theory. If B is a Boolean algebra then the Cantor-Bendixson ideals \(I_{\alpha}\) are defined inductively as follows. Let \(I_ 0=\{0\}\) and let \(I_{\alpha +1}\) be the ideal generated by \(I_{\alpha}\) together with all \(b\in B\) such that \(b/I_{\alpha}\) is an atom in \(B/I_{\alpha}\). For limit ordinals \(\lambda\) put \(I_{\lambda}=\cup \{I_{\alpha}; \alpha \in \lambda \}\). If \(B=I_{\beta}\) for some \(\beta\) then B is called superatomic and the least such ordinal is called the height of B \((\beta =ht(B))\). Let \(wd_{\alpha}(B)\) be the cardinality of the set of atoms of \(B/I_{\alpha}\). The central notion of the paper is that of \(\kappa\)- thin-thickness. B is called \(\kappa\)-thin-thick if \(ht(B)=\kappa +1,\) \(wd_{\alpha}(B)=\kappa\) for all \(\alpha\equiv \kappa\) and \(wd_{\kappa}(B)=\kappa^+\). Using Mitchell’s model it is shown that if \(``ZFC+\exists \delta:\delta\) inaccessible” is consistent, then so is ZFC with the inexistence of \(\aleph_ 1\)-thin-thick superatomic Boolean algebras. The remainder of the paper is devoted to the proof that by forcing one can produce a thin-very tall superatomic Boolean algebra B (i.e., \(ht(B)=\aleph_ 2\), \(wd_{\alpha}(B)=\aleph_ 0\) for all \(\alpha \in \aleph_ 2)\). During the proofs the authors introduce some new interesting combinatorial principles.