  Given $k\ge 2$ 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
$\Omega(n^{k-1})$. 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 $\Omega(n^{k-1})$ 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, R\"odl and Schacht [J. Lond. Math. Soc., 2018] that
classifies the 3-graphs with vanishing Tur\'an density in quasi-random
$k$-graphs.
