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We perform three-dimensional (3D) general-relativistic magnetohydrodynamicsimulations to model the jet break-out from the ejecta expected to be producedin a binary neutron-star merger. The structure of the relativistic outflow fromthe 3D simulation confirms our previous results from 2D simulations, namely,that a relativistic magnetized outflow breaking out from the merger ejectaexhibits a hollow core of $\theta_{\rm core}\approx4^{\circ}$, an opening angleof $\theta_{\rm jet}\gtrsim10^{\circ}$, and is accompanied by a wind of ejectedmatter that will contribute to the kilonova emission. We also compute thenon-thermal afterglow emission of the relativistic outflow and fit it to thepanchromatic afterglow from GRB170817A, together with the superluminal motionreported from VLBI observations. In this way, we deduce an observer angle of$\theta_{\rm obs}= 35.7^{\circ  \,\,+1.8}_{\phantom{\circ \,\,}-2.2}$. We further compute the afterglowemission from the ejected matter and constrain the parameter space for ascenario in which the matter responsible for the thermal kilonova emission willalso lead to a non-thermal emission yet to be observed.

3D magnetised jet break-out from neutron-star binary merger ejecta: afterglow emission from the jet and the ejecta