  Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and
$A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions
of $F$ and $A$, under which there exists a holomorphic immersion (or a proper
holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb
C)\subset\Bbb C^n\setminus F$.
