We present an exact solution for a cluster growth model, describing chainlike histories with ordered bond measure and external constraint connected to maximum (1 g/cm3) densities.Similar clusters also appear in spin systems, e. g., in insulating (Eu"Sr~")S at [9] x && 0.13 (the percolation threshold).The spins of the Eu ions will form few component clusters [6]. The spin-spin interaction is of a superexchange type, vanishing after the sixth neighboring distance [25]. Therefore, in this disordered spin system, similar to the previous carbon gas case, the clusterization process is governed firstly by short-range conditions [24] and secondly by the thermal excitation acting as an external bond breaking process. Studies of the liquid-gas transition [26] in systems of hard dipolar spheres [10], with application in ferrofluids [27], phase transitions [26] also show similar clusterization effects at high T and low density, governed by the same short-range conditions and an external bond cutting energy [10,28]. It is evident that the short-range conditions are generic to all disordered systems, in which few component chainlike clusters are dominant.That is, the clusterization process must be governed by a unique statistical process, independent of the system in which it occurs.The existence of a generic cluster law, for given conditions, can also be reflected at a mathematical level. We define the cluster growth problem in a standard manner: A history is a sequence h = (s;) of M space positions of some elements 2 = {E;), i~M -1, where h is a connected set, called cluster of mass M. The set H(CM) has various possible histories with a property H that leads to the cluster CM. If q is an external constraint, connected to the clusterization process, our task is to find for the well-defined and fixed (H, ri) conditions the probability p(CM, g) that satisfies 1 g~p(Cst, g) = Lt gH&p"~p (h, g), thus explaining the presence of the CM clusters within the system. The calculation of p(CM, rl), within the frame of (H, g), is normally handled by numerical simulations starting from a relatively low [29] M, and the existence of clusters