Zero subsequences for classes of holomorphic functions: stability and the entropy of arcwise connectedness. II

Let $\Omega$ be a domain in the complex plane $\mathbb C$, $H(\Omega)$ the space of functions holomorphic in $\Omega$, and $\mathscr P$ a family of functions subharmonic in $\Omega$. Denote by $H_{\mathscr P}(\Omega)$ the class of functions $f\in H(\Omega)$ satisfying $|f(z)|\leq C_f\exp p_f(z)$ for all $z\in\Omega$, where $p_f\in\mathscr P$ and $C_f$ is a constant. Conditions are found ensuring that a sequence $\Lambda=\{\lambda_k\}\subset\Omega$ be a subsequence of zeros for various classes $H_{\mathscr P}(\Omega)$. As a rule, the results and the method are new already when $\Omega=\mathbb D$ is the unit circle and $\mathscr P$ is a system of radial majorants $p(z)=p(|z|)$.
We continue the enumeration of Part I.