We present QMD simulations of water in the ultra-high-pressure regime up to conditions typical for the deep interior of Jupiter and Saturn. We calculate the equation of state and the Hugoniot curve and study the structural properties via pair correlation functions and self-diffusion coefficients. In the ultradense superionic phase, we find a continuous transition in the protonic structure. With rising density, the mobile protons stay with increasing probability at the octahedral sites while leaving the ice X positions to the same degree unoccupied. Water forms a fluid dense plasma at the conditions of Jupiter's core (i.e., $20\text{ }000\text{ }\text{K}$, 50 Mbar, $11\text{ }\text{g}/{\text{cm}}^{3}$), while it may be superionic in the core of Saturn. We expect a substantial amount of superionic water inside Neptune.