We prove that for fixed k, every k-uniform hypergraph on n vertices and of minimum codegree at least n/2 + o(n) contains every spanning tight k-tree of bounded vertex degree as a subgraph. This generalises a well-known result of Komlos, Sarkozy and Szemeredi for graphs. Our result is asymptotically sharp. We also prove an extension of our result to hypergraphs that satisfy some weak quasirandomness conditions. (c) 2023 Elsevier Inc. All rights reserved.