Point clouds of diverse natures are needed for different geometric modeling and processing applications. In this work, we propose a new Generative Adversarial Network (GAN), called Dynamic Style-TreeGAN, for the generation of 3D point clouds with quasi-uniform distribution and limited computational costs. While existing GAN models usually do not focus on the design of the discriminator, we propose a novel discriminator based on dynamic graph convolutional networks that does not require a priori information on input data connectivity. A selection of numerical examples show that our Dynamic Style-TreeGAN compares favourably with respect to existing architectures by improving the scattered data configuration of the generated samples. The considered tests also show that the generated point clouds are well suited for geometric processing applications, such as boundary detection and surface reconstruction schemes. In the test phase of the considered examples, the computational cost of our generative model is comparable to the one of GANs without a graph-based discriminator.