Despite the recent advances in multi-task learning of dense prediction problems, most methods rely on expensive labelled datasets. We present a label efficient approach and look at jointly learning of multiple dense prediction tasks on partially annotated data (i.e. not all the task labels are available for each image), which we call multi-task partially-supervised learning. We propose a multi-task training procedure that successfully leverages task relations to supervise its multi-task learning when data is partially annotated. In particular, we learn to map each task pair to a joint pairwise task-space which enables sharing information between them in a computationally efficient way through another network conditioned on task pairs, and avoids learning trivial cross-task relations by retaining high-level information about the input image. We rigorously demonstrate that our proposed method effectively exploits the images with unlabelled tasks and outperforms existing semi-supervised learning approaches and related methods on three standard benchmarks.