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We prove that for $k \in \mathbb{N}$ and $d \leq 2k+2$, if a graph hasmaximum average degree at most $2k + \frac{2d}{d+k+1}$, then $G$ decomposesinto $k+1$ pseudoforests, where one of the pseudoforests has all connectedcomponents having at most $d$ edges.

On Decomposing Graphs Into Forests and Pseudoforests