We present two new parallel implementations of the tree-ensemble algorithms Random Forest (RF) and Extremely randomized trees (ERT) for emerging many-core platforms, e.g., contemporary graphics cards suitable for general-purpose computing (GPGPU). Random Forest and Extremely randomized trees are ensemble learners for classification and regression. They operate by constructing a multitude of decision trees at training time and outputting a prediction by comparing the outputs of the individual trees. Thanks to the inherent parallelism of the task, an obvious platform for its computation is to employ contemporary GPUs with a large number of processing cores. Previous parallel algorithms for Random Forests in the literature are either designed for traditional multi-core CPU platforms or early history GPUs with simpler hardware architecture and relatively few number of cores. The new parallel algorithms are designed for contemporary GPUs with a large number of cores and take into account aspects of the newer hardware architectures as memory hierarchy and thread scheduling. They are implemented using the C/C++ language and the CUDA interface for best possible performance on NVidia-based GPUs. An experimental study comparing with the most important previous solutions for CPU and GPU platforms shows significant improvement for the new implementations, often with several magnitudes.