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We study how well different types of approaches generalise in the task of 3D hand pose estimation under single hand scenarios and hand-object interaction. We show that the accuracy of state-of-the-art methods can drop, and that they fail mostly on poses absent from the training set. Unfortunately, since the space of hand poses is highly dimensional, it is inherently not feasible to cover the whole space densely, despite recent efforts in collecting large-scale training datasets. This sampling problem is even more severe when hands are interacting with objects and/or inputs are RGB rather than depth images, as RGB images also vary with lighting conditions and colors. To address these issues, we designed a public challenge (HANDS'19) to evaluate the abilities of current 3D hand pose estimators (HPEs) to interpolate and extrapolate the poses of a training set. More exactly, HANDS'19 is designed (a) to evaluate the influence of both depth and color modalities on 3D hand pose estimation, under the presence or absence of objects; (b) to assess the generalisation abilities w.r.t. four main axes: shapes, articulations, viewpoints, and objects; (c) to explore the use of a synthetic hand model to fill the gaps of current datasets. Through the challenge, the overall accuracy has dramatically improved over the baseline, especially on extrapolation tasks, from 27mm to 13mm mean joint error. Our analyses highlight the impacts of: Data pre-processing, ensemble approaches, the use of a parametric 3D hand model (MANO), and different HPE methods/backbones.