Bayesian networks based on mixtures of polynomials (MoPs) are used to model multivariate hybrid or continuous probability distributions. MoPs try to provide a flexible yet simple model to deal with probabilistic reasoning, approximating complex or empirical probability distributions. We review the main models based on MoPs in the literature, introducing the mixtures of polynomials with tails (tMoPs) and derive analytically their main statistical properties: (cumulative) distribution function, moments, variance and moment-generating function. Also, we present an algorithm for learning a tMOPs density from data. This learning algorithm is tested with several standard probability distributions. In these experiments, the tMOPs models yield satisfactory results in comparison to other MoPs available alternatives. Finally, we sketch the process of building a meta-model that can directly provide a tMOPs expression for a specific density among a given family. This idea is tested with the well-known Beta distribution (two shape parameters), giving promising results.