Splittings and calculational techniques for higher THH

Tensoring finite pointed simplicial sets X with commutative ring spectra R yields important homology theories such as (higher) topological Hochschild homology and torus homology. We prove several structural properties of these constructions relating (Formula Presented) and we establish splitting results. This allows us, among other important examples, to determine THH _* ^[n]�(Z/p ^m; Z/p) for all n ≥ 1 and for all m ≥ 2.