We propose a method to build trees and forests when the response is a non-homogeneous Poisson process with excess zeros, based on two forests. The first one is used to estimate the probability of having a zero. The second forest is used to estimate the Poisson parameter using trees built with a splitting criterion derived from the zero truncated non-homogeneous Poisson likelihood. Simulation studies show that the proposed method performs well in hurdle (zero-altered) and zero-inflated settings.