  Let $D$ be a nonempty domain in $\mathbb C^n$. We give a scale of necessary
conditions for the distribution of the zero set of holomorphic function $f$ on
domain $D\subset {\mathbb C}^n$ under a restriction on its growth $|f|\leq \exp
M$, where $M\not\equiv -\infty$ is a subharmonic function. If $n=1$, $D\neq
\mathbb C$ is simply connected, and $M$ is continuous, then this conditions are
sufficient.
