I wonder if the notion of "maximal submanifold" exists or is relevant? I'm surprised because I found pretty much nothing about it on the web (after a quick search).
The definition, which seems natural to me, would be something like: Let $M$ be a (smooth, say) manifold. A maximal submanifold in $M$ is a connected submanifold $N$ (smoothly embedded, say) such that there is no other connected submanifold $N'$ of $M$ such that $\dim N' = \dim N$ and $N'$ strictly contains $N$.