This paper investigates the situation where a (large) group of terminals can be connected simultaneously to several base stations using distinct wireless technologies. We introduce and solve the problem of optimally sharing the mobile transmit power between different systems. Key results from asymptotic random matrix theory (when the number of users and the dimensions of different systems increase) allow us to derive the best power allocation scheme in the sense of the sum-capacity of the overall system, for which the uplink is equivalent to a parallel fading multiple access channel. Moreover, we provide an iterative algorithm to solve the power allocation algorithm. Simulations for a finite number of users validate the asymptotic claims.