In this article we continue the research, carried out in \cite{zajac}, on computing $*$-product of domains $\CC^N$. Assuming that $0\in G\subset\CC^N$ is an arbitrary Runge domain and D\subset\CC^N$ a bounded, smooth linearly convex (or non-decreasing union such ones), establish geometric relation between $D*G$ another $\CC^N$ which 'extremal' (in appropriate sense) with respect to special coef...