  We calculate the exact stationary distribution of the one-dimensional
zero-range process with open boundaries for arbitrary bulk and boundary hopping
rates. When such a distribution exists, the steady state has no correlations
between sites and is uniquely characterized by a space-dependent fugacity which
is a function of the boundary rates and the hopping asymmetry. For strong
boundary drive the system has no stationary distribution. In systems which on a
ring geometry allow for a condensation transition, a condensate develops at one
or both boundary sites. On all other sites the particle distribution approaches
a product measure with the finite critical density \rho_c. In systems which do
not support condensation on a ring, strong boundary drive leads to a condensate
at the boundary. However, in this case the local particle density in the
interior exhibits a complex algebraic growth in time. We calculate the bulk and
boundary growth exponents as a function of the system parameters.
