Kinship face synthesis is an increasingly popular topic within the computer vision community, particularly the task of predicting the child appearance using parental images. Previous work has been limited in terms of model capacity and inadequate training data, which comprised of low-resolution and tightly cropped images, leading to lower synthesis quality. In this paper, we propose ChildNet, a method for kinship face synthesis that leverages the facial image generation capabilities of a state-of-the-art Generative Adversarial Network (GAN), and resolves the aforementioned problems. ChildNet is designed within the GAN latent space and is able to predict a child appearance that bears high resemblance to real parents' children. To ensure fine-grained control, we propose an age and gender manipulation module that allows precise manipulation of the child synthesis result. ChildNet is capable of generating multiple child images per parent pair input, while providing a way to control the image generation variability. Additionally, we introduce a mechanism to control the dominant parent image. Finally, to facilitate the task of kinship face synthesis, we introduce a new kinship dataset, called Next of Kin. This dataset contains 3690 high-resolution face images with a diverse range of ethnicities and ages. We evaluate ChildNet in comprehensive experiments against three competing kinship face synthesis models, using two kinship datasets. The experiments demonstrate the superior performance of ChildNet in terms of identity similarity, while exhibiting high perceptual image quality. The source code for the model is publicly available at: https://github.com/MartinPernus/ChildNet.