wide family of surfaces of elliptic type. Although these estimates are not optimal, the existence of such height estimates with respect to planes constitute a fundamental tool for studying the behaviour of complete embedded surfaces.

Following the ideas developed by Rosenberg and Sa Earp in [@RoS], we show that the theory developed by Korevaar, Kusner, Meeks and Solomon [@KKMS; @KKS; @M] for constant mean curvature surfaces in $\r^3$ and $\h^3$ remains valid for some families of surfaces satisfying the maximum principle (Theorem \[finales\]).

In particular, when Theorem \[finales\] is applied to a properly embedded Weingarten surface $\Sigma$ of elliptic type satisfying $H=f(H^2-K)$ in $\r^3$ or $\h^3$, we obtain: If $\Sigma$ has finite topology and $k$ ends, then $k\geq 2$, $\Sigma$ is rotational if $k=2$, and $\Sigma$ is contained in a slab if $k=3$.

To finish the paper, we study the problem of classifying Weingarten surfaces of elliptic type satisfying $H=f(H^2-K)$ in $\r^3$ such that $K$ does not change signs [@ST3]. We show that, in the above conditions, if $\Sigma$ is a complete surface with $K\geq0$ then it must be a totally umbilical sphere, a plane or a right circular cylinder, and if $\Sigma$ is properly embedded and $K\leq 0$, then 