  We consider the one-dimensional partially asymmetric zero range process where
the hopping rates as well as the easy direction of hopping are random
variables. For this type of disorder there is a condensation phenomena in the
thermodynamic limit: the particles typically occupy one single site and the
fraction of particles outside the condensate is vanishing. We use extreme value
statistics and an asymptotically exact strong disorder renormalization group
method to explore the properties of the steady state. In a finite system of $L$
sites the current vanishes as $J \sim L^{-z}$, where the dynamical exponent,
$z$, is exactly calculated. For $0<z<1$ the transport is realized by $N_a \sim
L^{1-z}$ active particles, which move with a constant velocity, whereas for
$z>1$ the transport is due to the anomalous diffusion of a single Brownian
particle. Inactive particles are localized at a second special site and their
number in rare realizations is macroscopic. The average density profile of
inactive particles has a width of, $\xi \sim \delta^{-2}$, in terms of the
asymmetry parameter, $\delta$. In addition to this, we have investigated the
approach to the steady state of the system through a coarsening process and
found that the size of the condensate grows as $n_L \sim t^{1/(1+z)}$ for large
times. For the unbiased model $z$ is formally infinite and the coarsening is
logarithmically slow.
