Together with Chun Yin Lam, after the derivation of the continuous generalized exchange-driven growth model in arXiv:2503.21572, we continue the study of the existence and uniqueness of solutions for kernels with superlinear growth at infinity and singularity at the origin. Moreover, we show the non-existence of solutions for kernels with sufficiently rapid growth. The latter result is shown via the finite-time gelation and instantaneous gelation in the sense of moment blow-up. For details see arXiv:2509.05262.