Some years ago Mistuhiro Shishikura showed how the use of some special trees and be useful to study existence of special holomorphic dynamical systems. Then, the same kind of trees have been introduced by DeMarco-McMullen to study some hyperbolic components of the space of polynomials dynamical systems. After the work of Jan Kiwi on Berkovich space, I introduced in my thesis a vocabulary to propose a definition of dynamical systems between trees of spheres in order to unify all of these points of view. With this vocabulary, Jan Kiwi's results have been reproved and I showed with Cui Guizhen how to improve our knowledge of special kind of behavior when taking sequences of rational maps diverging in the natural associated Moduli space.