We are interested in the linearization of some families of analytic germs. By generalizing definitions and properties of transfinite diameter, we obtain a polynomial majoration theorem that works both for the complex and the p-adic numbers. Then these tools are used to give a new proof of Perez-Marco's theorem about the linearization of non-resonant families of analytic germs under a polynomial perturbation. This proof allows the generalization of Perez-Marco's theorem to the p-adic case. Furthermore, with this new point of view, we obtain a diophantine information and give new examples of non linearizable germs. We generalize this theorem to the case of a perturbation with rational maps. Finally, a reasonant case is studied and we give a new proof, more elementary, of some properties of the centralizer of germs tangent to identity.
