  Let $1\leq p\leq n$ be two positive integers. For a linearly nondegenerate
holomorphic mapping $f\colon\mathbb{C}^p\rightarrow\mathbb{P}^n(\mathbb{C})$ of
maximal rank intersecting a family of hyperplanes in general position, we
obtain a Cartan's type Second Main Theorem in which the counting functions are
truncated to level $n+1-p$. Our result strengthens the classical results of
Stoll and Vitter, and interpolates the important works of Cartan and
Carlson-Griffiths.
