  We analyze the condensation phase transitions in out-of-equilibrium complex
networks in a unifying framework which includes the nonlinear model and the
fitness model as its appropriate limits. We show a novel phase structure which
depends on both the fitness parameter and the nonlinear exponent. The
occurrence of the condensation phase transitions in the dynamical evolution of
the network is demonstrated by using Bianconi-Barabasi method. We find that the
nonlinear and the fitness preferential attachment mechanisms play important
roles in formation of an interesting phase structure.
