This paper adjusts a mathematical decomposition approach to the AC power flow problem in power systems with interconnected areas operated by diferent transmission system operators (TSO). The proposed strategy allows finding the operation point of a particular area without explicit knowledge of network data of the other interconnected areas, being only necessary to exchange border information related to the tie-lines between areas. The methodology is based on the decomposition of the first-order optimality conditions of the AC power flow, which is formulated as a nonlinear programming problem. To allow better visualization of the concept of independent operation of each TSO, an artificial neural network have been used to simulate the border information calculation of the interconnected TSOs. A multi-area Power Flow tool can be seen as a basic building block able to address a large number of problems under a multi-TSO competitive market philosophy. The IEEE RTS-96 power system is used in order to show the operation and effectiveness of the decentralized AC Power Flow.