Constant mean curvature surfaces in ${\mathbb{H}}^2\times \mathbb{R}$ with boundary in two parallel planes

Given $H\in [0,\mathrm{\infty }),$ some sufficient conditions for existence of CMC $H$ graphs with boundary in two parallel planes of ${\mathbb{H}}^2\times \mathbb{R}$ are presented. Height estimates for outwards-oriented CMC surfaces (horo)cyllindrically bounded are also exhibited.