We study a one-dimensional anisotropic exclusion process describing particles injected at the origin, moving to the right on a chain of L sites and being removed at the (right) boundary. We construct the steady state and compute the density profile, exact expressions for all equal-time n-point density correlation functions and the time-dependent two-point function in the steady state as functions of the injection and absorption rates. We determine the phase diagram of the model and compare our

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... esults with predictions from dynamical scaling and discuss some conjectures for other exclusion models.