  Let $D$ be a digraph, let $p \geq 1$ be an integer, and let $f: V(D) \to
\mathbb{N}_0^p$ be a vector function with $f=(f_1,f_2,\ldots,f_p)$. We say that
$D$ has an $f$-partition if there is a partition $(D_1,D_2,\ldots,D_p)$ into
induced subdigraphs of $D$ such that for all $i \in [1,p]$, the digraph $D_i$
is weakly $f_i$-degenerate, that is, in every non-empty subdigraph $D'$ of
$D_i$ there is a vertex $v$ such that $\min\{d_{D'}^+(v), d_{D'}^-(v)\} <
f_i(v)$. In this paper, we prove that the condition $f_1(v) + f_2(v) + \ldots +
f_p(v) \geq \max \{d_D^+(v),d_D^-(v)\}$ for all $v \in V(D)$ is almost
sufficient for the existence of an $f$-partition and give a full
characterization of the bad pairs $(D,f)$. Moreover, we describe a polynomial
time algorithm that (under the previous conditions) either verifies that
$(D,f)$ is a bad pair or finds an $f$-partition. Among other applications, this
leads to a generalization of Brooks' Theorem as well as the list-version of
Brooks' Theorem for digraphs, where a coloring of digraph is a partition of the
digraph into acyclic induced subdigraphs. We furthermore obtain a result
bounding the $s$-degenerate chromatic number of a digraph in terms of the
maximum of maximum in-degree and maximum out-degree.
