  We prove a version of the strong half-space theorem between the classes of
recurrent minimal surfaces and complete minimal surfaces with bounded curvature
of $\mathbb{R}^{3}_{\raisepunct{.}}$ We also show that any minimal hypersurface
immersed with bounded curvature in $M\times \R_+$ equals some $M\times \{s\}$
provided $M$ is a complete, recurrent $n$-dimensional Riemannian manifold with
$\text{Ric}_M \geq 0$ and whose sectional curvatures are bounded from above.
For $H$-surfaces we prove that a stochastically complete surface $M$ can not be
in the mean convex side of a $H$-surface $N$ embedded in $\R^3$ with bounded
curvature if $\sup \vert H_{_M}\vert < H$, or ${\rm dist}(M,N)=0$ when $\sup
\vert H_{_M}\vert = H$. Finally, a maximum principle at infinity is shown
assuming $M$ has non-empty boundary.
