Given $M,N$, $R$-modules, it is standard verification that $-\otimes Z$ is left adjoint to $Hom(Z,-)$.
If we have more structure, particularly if $\mathcal{A}$ and $\mathcal{B}$ are C*-algebras, choosing any suitable norm in the purely algebraic tensor product (so that the product is still a C*-algebra), what more adjunctions arise from this construction ?