The superellipsoid model is a rich geometric model and is convenient to study the particle shape effects on random packings. The particle shape significantly influences the macroscopic and microscopic structure properties of random packings. In this work, we find uniform and decoupled shape effects on the maximally dense random packings (MDRPs) of hard superellipsoids. Slightly changing the surface shape or elongating (compressing) the particles may influence the random packing density significantly. The influences of surface shape parameter p and aspect ratio w on the random packing densities are decoupled. For the aspect ratio effects, all the packing density curves show "M" type with various p. Meanwhile, the aspect ratio effects are applicable to all the symmetric particles with three equal main cross sections when w = 1.0. For the surface shape effects, the packing density curve is also in "M" type with various w. The maximum of the random packing density is obtained at p approximate to 0.7, 2.0 and w approximate to 0.7, 1.5. Moreover, we obtain the MDRPs of hard superellipsoids via the inverse Monte Carlo packing method with a wide range of the surface shape parameter. The normalized local cubatic order parameter and a new normalized local bond-orientational order parameter are used to evaluate the order degrees of orientations and bond-orientations in random packings, respectively. The local analyses of the MDRPs of superellipsoids are carried out via the Voronoi tessellation. Two linear relationships between the mean and standard deviation of the reduced Voronoi cell volumes are obtained. Our findings should lead to a better understanding of random packings and are helpful in guiding the granular material design. (C) 2018 Elsevier B.V. All rights reserved.