  We prove that any quasirandom uniform hypergraph $H$ can be approximately
decomposed into any collection of bounded degree hypergraphs with almost as
many edges. In fact, our results also apply to multipartite hypergraphs and
even to the sparse setting when the density of $H$ quickly tends to $0$ in
terms of the number of vertices of $H$. Our results answer and address
questions of Kim, K\"uhn, Osthus and Tyomkyn; and Glock, K\"uhn and Osthus as
well as Keevash.
  The provided approximate decompositions exhibit strong quasirandom properties
which is very useful for forthcoming applications. Our results also imply
approximate solutions to natural hypergraph versions of long-standing graph
decomposition problems, as well as several decomposition results for
(quasi)random simplicial complexes into various more elementary simplicial
complexes such as triangulations of spheres and other manifolds.
