  If $(M,g)$ and $(\hM,\hg)$ are two smooth connected complete oriented
Riemannian manifolds of dimensions $n$ and $\hn$ respectively, we model the
rolling of $(M,g)$ onto $(\hM,\hg)$ as a driftless control affine systems
describing two possible constraints of motion: the first rolling motion
$\Sigma_{NS}$ captures the no-spinning condition only and the second rolling
motion $\Sigma_{R}$ corresponds to rolling without spinning nor slipping. Two
distributions of dimensions $(n + \hn)$ and $n$, respectively, are then
associated to the rolling motions $\Sigma_{NS}$ and $\Sigma_{R}$ respectively.
This generalizes the rolling problems considered in \cite{ChitourKokkonen1}
where both manifolds had the same dimension. The controllability issue is then
addressed for both $\Sigma_{NS}$ and $\Sigma_{R}$ and completely solved for
$\Sigma_{NS}$. As regards to $\Sigma_{R}$, basic properties for the reachable
sets are provided as well as the complete study of the case $(n,\hn)=(3,2)$ and
some sufficient conditions for non-controllability.
