  Let $\mathcal{F}$ be a family of $r$-uniform hypergraphs, and let $H$ be an
$r$-uniform hypergraph. Then $H$ is called $\mathcal{F}$-free if it does not
contain any member of $\mathcal{F}$ as a subhypergraph. The Tur\'{a}n number of
$\mathcal{F}$, denoted by $ex_r(n,\mathcal{F})$, is the maximum number of
hyperedges in an $\mathcal{F}$-free $n$-vertex $r$-uniform hypergraph. Our
current results are motivated by earlier results on Tur\'{a}n numbers of star
forests and hypergraph star forests. In particular, Lidick\'{y}, Liu and Palmer
[Electron. J. Combin. 20 (2013)] determined the Tur\'{a}n number $ex(n,F)$ of a
star forest $F$ for sufficiently large $n$. Recently, Khormali and Palmer
[European. J. Combin. 102 (2022) 103506] generalized the above result to three
different well-studied hypergraph settings, but restricted to the case that all
stars in the hypergraph star forests are identical. We further generalize these
results to general hypergraph star forests.
