  Recent progress in cooling and trapping of polarized clouds of chromium
$^{52}Cr$, dysprosium $^{164}Dy$ and erbium $^{168}Er$ opens a road-map to
quantum systems where shapes of inter-particle interactions can be customized.
The main purpose of this work is to get a deeper insight on a role which the
overall shape of the inter-particle interaction plays in a context of trapped
ultra-cold bosons. We show that strong inter-particle repulsion inevitably
leads to multi-hump fragmentation of the ground state. The fragmentation
phenomenon is universal -- it takes place in traps of different dimensionality
and topologies and for very broad classes of repulsive inter-particle
potentials. The physics behind is identified and explained.
