Given k ≥ 2 and two k-graphs (k-uniform hypergraphs) F and H, an F -factor in H is a set of vertex disjoint copies of F that together covers the vertex set of H. Lenz and Mubayi [J. Combin. Theory Ser. B, 2016 ] studied the F -factor problem in quasi-random k-graphs with minimum degree Ω(n k−1 ). They posed the problem of characterizing the k-graphs F such that every sufficiently large quasi-random k-graph with constant edge density and minimum degree Ω(n k−1 ) contains an F -factor, and in particular, they showed that all linear k-graphs satisfy this property.In this paper we prove a general theorem on F -factors which reduces the F -factor problem of Lenz and Mubayi to a natural sub-problem, that is, the F -cover problem. By using this result, we answer the question of Lenz and Mubayi for those F which are k-partite k-graphs, and for all 3-graphs F , separately. Our characterization result on 3-graphs is motivated by the recent work of Reiher, Rödl and Schacht [J. Lond. Math. Soc., 2018 ] that classifies the 3-graphs with vanishing Turán density in quasi-random k-graphs.

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