Suppose $F: \mathbb{C}^n \to \mathbb{C}^n$ is a surjective function such that $F$ is defined by a polynomial in each coordinate, i.e. $$ F = (f_1,\ldots,f_n) \quad f_i \in \mathbb{C}[x_1,\ldots,x_n] \: \forall i \leq n $$
I know that for $n = 1$, $F$ is simply a polynomial function in one variable, and therefore the fact that $F$ is surjective implies $F$ is proper. Furthermore I know that for $n > 1$, each $f_i$ is not proper as a map $f_i: \mathbb{C}^n \to \mathbb C$. My question is, under what circumstances is the map $F$ a proper map in general? Is this dependent or independent of whether $F$ is a submersion?