  We study the condensation phenomenon in a zero range process on scale-free
networks. We show that the stationary state property depends only on the degree
distribution of underlying networks. The model displays a stationary state
phase transition between a condensed phase and an uncondensed phase, and the
phase diagram is obtained analytically. As for the dynamical property, we find
that the relaxation dynamics depends on the global structure of underlying
networks. The relaxation time follows the power law $\tau \sim L^z$ with the
network size $L$ in the condensed phase. The dynamic exponent $z$ is found to
take a different value depending on whether underlying networks have a tree
structure or not.
