Naturally, the gravitational force attracts them at greater distances. Therefore, there will be a point where the attraction and repulsion are equal, creating a 'resting point' of least resistance. An example of a globular lattice of about 200 particles can be seen in the 'Pocket Universe' logo at the top of this page. If the mass is high enough, perhaps more than one particle will occupy each spot. Further, if the gravitational force is around the same magnitude as the pressure force, then particles will jostle for position by jumping in and out of the points of least resistance.
Some particles can even pass through the entire structure uninhibited if they take the correct path.
Note that friction is required to make the particles settle, which will absorb most of the energy. Rotational friction will then slowly sap the remaining energy. This has a parallel with the formation of stars. Interestingly, when two such stars become close to each other, they exert tidal forces on each other. This bulging can cause particles to be forced away from its host, losing them to the other star.