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A series of specimens of increasing diameter (7 to 10 A) that were cut from a periodic diamond lattice and involved up to 250 atoms was considered. The formation of graphite-like shells was modeled by adding different structure blocks to the relaxed diamond-core Cn clusters. The structure blocks were composed of fused five- and six-membered rings and had either convex or planar configuration. Diamond-like Cn systems resemble balls with bullate convexoconcave surfaces that look as if smooth spheres are covered with randomly arranged excrescences. Depending on the atomic size and configuration, surface protuberances can either be stable or highly unstable. Furthermore, depending on the coordination types of atoms involved, surface fragments can either be polarized or non-polar, which determines the motive forces of the interactions between them and with foreign particles. Graphite-like shells preserve to a more or less degree the features typical of carbon nanotube walls depending on the local curvature of the core and the prevailing coordination types of its surface atoms. The motive forces of aggregation of model carbon particles can be different. There are actually at least two principal possibilities, namely (i) when surfaces of particles brought in contact are formed of predominantly hexagons, which are more or less distorted compared to those constituting nanotube surfaces or fullerene faces and (ii) when faceted interacting surfaces involve tri- to pentagon fragments