  We extend the theory of separately holomorphic mappings between complex
analytic spaces. Our method is based on Poletsky theory of discs, Rosay Theorem
on holomorphic discs and our recent joint-work with Pflug on cross theorems in
dimension 1. It also relies on our new technique of conformal mappings and a
generalization of Siciak's relative extremal function.
  Our approach illustrates the unified character: ``From local informations to
global extensions". Moreover, it avoids systematically the use of the classical
method of doubly orthogonal bases of Bergman type.
