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We prove a uniform version of non-Archimedean Yomdin-Gromov parametrizationsin a definable context with algebraic Skolem functions in the residue field.The parametrization result allows us to bound the number of F_q[t]-points ofbounded degrees of algebraic varieties, uniformly in the cardinality q of thefinite field F_q and the degree, generalizing work by Sedunova for fixed q. Wealso deduce a uniform non-Archimedean Pila-Wilkie theorem, generalizing work byCluckers-Comte-Loeser.

Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fields