Factors in randomly perturbed hypergraphs

We determine, up to a multiplicative constant, the optimal number of random edges that need to be added to a k-graph H with minimum vertex degree (Formula presented.) to ensure an F-factor with high probability, for any F that belongs to a certain class (Formula presented.) of k-graphs, which includes, for example, all k-partite k-graphs, (Formula presented.) and the Fano plane. In particular, taking F to be a single edge, this settles a problem of Krivelevich, Kwan, and Sudakov. We also address the case in which the host graph H is not dense, indicating that starting from certain such H is essentially the same as starting from an empty graph (namely, the purely random model).