  Let K be a non archimedean algebraically closed field of characteristic pi
complete for its ultrametric absolute value. In a recent paper by Escassut and
Yang, polynomial decompositions P(f)=Q(g) for meromorphic functions f, g on K
(resp. in a disk) have been considered, and for a class of polynomials P, Q,
estimates for the Nevanlinna function T(r,f) have been derived. In the present
paper we consider as a generalization rational decompositions of meromorphic
functions. In the case, where f, g are analytic functions, the Second
Nevanlinna Theorem yields an analogue result as in the mentioned paper.
However, if they are meromorphic, non trivial estimates for T(r,f) are more
sophisticated.
