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A proper vertex coloring of a simple graph is $k$-forested if the graphinduced by the vertices of any two color classes is a forest with maximumdegree less than $k$. A graph is $k$-forested $q$-choosable if for a given listof $q$ colors associated with each vertex $v$, there exists a $k$-forestedcoloring of $G$ such that each vertex receives a color from its own list. Inthis paper, we prove that the $k$-forested choosability of a graph with maximumdegree $\Delta\geq k\geq 4$ is at most $\lceil\frac{\Delta}{k-1}\rceil+1$,$\lceil\frac{\Delta}{k-1}\rceil+2$ or $\lceil\frac{\Delta}{k-1}\rceil+3$ if itsmaximum average degree is less than 12/5, $8/3 or 3, respectively.

k-forested choosability of graphs with bounded maximum average degree