We investigate the dependence of the gamma-ray burst (GRB) jet structure and its evolution on the properties of the accreting torus in the central engine. Our models numerically evolve the accretion disk around a Kerr black hole using three-dimensional general relativistic magnetohydrodynamic simulations. We use two different analytical hydrodynamical models of the accretion disk, based on the Fishbone–Moncrief and Chakrabarti solutions, as our initial states for the structure of the collapsar

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... isk and the remnant after a binary neutron star (BNS) merger, respectively. We impose poloidal magnetic fields of two different geometries upon the initial stable solutions. We study the formation and evolution of the magnetically arrested disk state and its effect on the properties of the emitted jet. The jets produced in our models are structured and have a relatively hollow core and reach higher Lorentz factors at an angle ≳9° from the axis. The jet in our short GRB model has an opening angle of up to ∼25° while our long GRB engine produces a narrower jet, of up to ∼11°. We also study the time variability of the jets and provide an estimate of the minimum variability timescale in our models. The application of our models to the GRB jets in the BNS postmerger system and to the ultrarelativistic jets launched from collapsing stars are briefly discussed.