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We prove that for fixed $k$, every $k$-uniform hypergraph on $n$ vertices andof minimum codegree at least $n/2+o(n)$ contains every spanning tight $k$-treeof bounded vertex degree as a sub\-graph. This generalises a well-known resultof Koml\'os, S\'ark\"ozy and Szemer\'edi for graphs. Our result isasymptotically sharp. We also prove an extension of our result to hypergraphsthat satisfy some weak quasirandomness conditions.

Dirac-type conditions for spanning bounded-degree hypertrees