Constant Mean Curvature Surfaces in ${\mathbb{M}}^2(c)\times \mathbb{R}$ and Finite Total Curvature

We consider surfaces with parallel mean curvature vector field and finite total curvature in product spaces of type ${\mathbb{M}}^n(c)\times \mathbb{R}$, where ${\mathbb{M}}^n(c)$ is a space form, and characterize certain of these surfaces. When $n=2$, our results are similar to those obtained in \cite{bds} for surfaces with constant mean curvature in space forms.