Bézier surfaces have been widely employed in the designing of complex scenes with high-quality results. Nevertheless, parametric surfaces cannot be directly rendered in the current GPUs of modern handheld devices. This work proposes a non-adaptive method for tessellating Bézier surfaces on a GPU without primitive generator, such as the GPUs implemented in handled devices. Our technique is based on the utilization of a parametric map of virtual vertices, and its operation can be adapted to the hardware resources available in the GPU by tuning a series of parameters. Additionally, an analysis of the most relevant hardware constraints in the graphics hardware of the current handheld devices has been carried out. As those constraints prevent interactive high-quality results from being achieved, even with our proposal, we present an algorithmic approach focused on the real-time rendering on future handheld devices.