We study families$G(\lambda,\cdot)$ of entire functions that are approximated by a sequence offamilies $G_n(\lambda,\cdot)$ of entire functions,where $\lambda\in\C$ is a parameter. In order to control the dynamics,the families are assumed to be of the same constant finite type.In this setting we provethe convergence of the hyperbolic components in parameter space as kernelsin the sense of Carathéodory.