Three-dimensional numerical simulations of thermo-chemical mantle convection with multiple phase transitions (olivine-spinel-perovskite-post perovskite) are used to investigate the morphology of compositional and post-perovskite (PPV) boundary structures above the core-mantle boundary (CMB). Compositionally-dense subducted MORB partially segregates above the CMB forming ridge-like dense piles, morphologically similar to structures in previous spherical or Cartesian studies in which a dense layer was inserted a priori. An anti-correlation is observed between regions where a thick post-perovskite layer occurs and regions containing piles of dense material, as in our previous two-dimensional study. Lateral variations in the thickness or occurrence of a PPV layer cause very strong seismic shear-wave velocity anomalies which may dominate thermal or composition-related seismic heterogeneity in the depth range where the variable PPV boundary occurs, and also generate sharp-sided structures as observed seismologically. Both compositional and PPV effects may be necessary to simultaneously explain large-scale heterogeneity and the global distribution of the discontinuity atop D″.