We study the existence and uniqueness problem of compact minimal vertical graphs in H n × R, n ≥ 2, over bounded domains in the slice H n × {0}, with non-connected boundary having a finite number of C 0 hypersufaces homeomorphic to the sphere S n−1 , with prescribed bounded continuous boundary data, under hypotheses relating those data and the geometry of the boundary. We show the nonexistence of compact minimal vertical graphs in H n × R having the boundary in two slices and the height greater than or equal to π/(2n − 2).