  We study two families of type II discrete multiple orthogonal polynomials on
an $r$-legged star-like set with respect to $r$ weight functions of Charlier
(Poisson distributions) and Meixner (negative binomial distributions),
respectively. We focus our attention on the structural properties such as the
raising operators, the Rodrigues-type formulas, and the explicit expressions of
the polynomial families as well as the coefficients of the nearest neighbor
recurrence relation. A limit relation between these families is given.
