  We examine the regime between crystalline and amorphous packings of
anisotropic objects on surfaces of different genus by continuously varying
their size distribution or shape from monodispersed spheres to bidispersed
mixtures or monodispersed ellipsoidal particles; we also consider an
anisotropic variant of the Thomson problem with a mixture of charges. With
increasing anisotropy, we first observe the disruption of translational order
with an intermediate orientationally ordered hexatic phase as proposed by
Nelson, Rubinstein and Spaepen, and then a transition to amorphous state. By
analyzing the structure of the disclination motifs induced, we show that the
hexatic-amorphous transition is caused by the growth and connection of
disclination grain boundaries, suggesting this transition lies in the
percolation universality class in the scenarios considered.
