In some multiźtarget tracking applications, appearing targets are suitably modeled as spawning from existing targets. However, in the original cardinalized probability hypothesis density (CPHD) filter, this type of model is not included; instead appearing targets are modeled by spontaneous birth only. Recently, two versions of CPHD filter modeling spawning targets have already been developed, but these two methods are tractable only when the spawning targets cardinality distribution is restricted to be the Bernoulli distribution, the Poisson distribution or the Zero-inflated Poisson distribution. In this paper, we derive a generalized CPHD filter which is tractable and has no constraint of the cardinality distribution of the spawning targets, that is to say, the spawning targets cardinality distribution can be arbitrary. The derivation is based on the finite set statistics (FISST) and the Faa di bruno's determinant formula. Moreover, how this generalized CPHD filter degrades into the two previous versions is also given in this paper. The resulting filter is different from the original CPHD filter in two aspects: first, the prediction equation of the PHD function changes to be identical with that of the probability hypothesis density (PHD) filter; and second, the cardinality distribution prediction equation is now an expression including the cardinality distribution information of the spawning targets. Simulation results show that the proposed method can response much faster than the original CPHD filter in target number estimate when spawning targets appear, and has a much smaller cardinality estimate variance than the PHD filter and the original CPHD filter. A comparison considering the optimal sub-pattern assignment (OSPA) metric also demonstrates the good performance of the proposed method. The general explicit cardinality prediction equation for the CPHD filter modeling spawning targets is derived.The derivation is based on the famous Faa di bruno's determinant formula.A tractable recursion computation technique of the general cardinality prediction equation is proposed.