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Given positive integers $a\leq b \leq c$, let $K_{a,b,c}$ be the complete3-partite 3-uniform hypergraph with three parts of sizes $a,b,c$. Let $H$ be a3-uniform hypergraph on $n$ vertices where $n$ is divisible by $a+b+c$. Weasymptotically determine the minimum vertex degree of $H$ that guarantees aperfect $K_{a, b, c}$-tiling, that is, a spanning subgraph of $H$ consisting ofvertex-disjoint copies of $K_{a, b, c}$. This partially answers a question ofMycroft, who proved an analogous result with respect to codegree for$r$-uniform hypergraphs for all $r\ge 3$. Our proof uses a lattice-basedabsorbing method, the concept of fractional tiling, and a recent result onshadows for 3-graphs.

Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs