  We prove $S$-arithmetic inhomogeneous Khintchine type theorems on analytic
nondegenerate manifolds. The divergence case, which constitutes the main
substance of this paper, is proved in the general context of Hausdorff measures
using ubiquitous systems. For $S$ consisting of more than one prime, finite or
infinite, the divergence results are new even in the homogeneous setting. We
also prove the convergence case of the theorem, including in particular, the
$S$-arithmetic inhomogeneous counterpart of the Baker-Sprind\v{z}uk conjectures
using nondivergence estimates for flows on homogeneous spaces in conjunction
with the transference principle of Beresnevich and Velani.
