In recent years, many researchers have studied the distributions of the Demmel (or the scaled) condition numbers (DCN) of complex Wishart matrices. In this paper, several new distributional properties of the distribution of the Demmel condition number of complex Wishart matrices are presented. The limiting distributions of the standardized extreme order statistics are given. Since the truncated distributions arise in practical statistics where the ability of record observations is limited to a given threshold or within a specified range, there has been a great interest, in recent years, in the characterizations of probability distributions by truncated moments. Before a particular probability distribution model is applied to fit the realworld data, it is necessary to confirm whether the given continuous probability distribution satisfies the underlying requirements by its characterization. Therefore, in this paper, some characterizations of the distribution of DCN are also shown. We hope that the findings of this paper will be quite useful in many fields of pure and applied sciences, such as, probability, statistics, multivariate statistics, linear algebra, operator algebra theory, actuarial science, physics, wireless communications, and polarimetric synthetic aperture radar (PolSAR), among others.