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Fix a graph $F$. We say that a graph is {\it $F$-free} if it does not contain$F$ as a subgraph. The {\it Tur\'an number} of $F$, denoted $\mathrm{ex}(n,F)$,is the maximum number of edges possible in an $n$-vertex $F$-free graph. Thestudy of Tur\'an numbers is a central problem in graph theory. The goal of thispaper is to generalize a theorem of Lidick\'y, Liu and Palmer [{\it Electron.\J.\ of Combin.}\ {\bf 20} (2016)] that determines $\mathrm{ex}(n,F)$ for $F$ aforest of stars. In particular, we consider generalizations of the problem tothree different well-studied hypergraph settings and in each case we prove anasymptotic result for all reasonable parameters defining our "star forests".

Tur\'an numbers for hypergraph star forests