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In this article, we explore the dynamics of accretion structures encircling spherically symmetric black holes, comparing three accretion disk models with distinct angular momentum profiles: (i) the geometrically thin Keplerian disk, (ii) the Fishbone-Moncrief torus; and (iii) the Polish Doughnut. Employing general relativistic magnetohydrodynamics simulations with the High Accuracy Relativistic Magnetohydrodynamics code, we investigate these three models, considering the magnetic field's influence on the accretion disk angular momentum redistribution. We show that the magnetic field is a key factor in accretion disk structures, especially in regions with lower mass density. Our investigation verifies the well-established fact that the presence of a magnetic field significantly influences the accretion rate and its temporal variability.