In paper 1 of this series we described an analytical-numerical method to predict deterministically solute transport under uncertainty. The method is based on a unified Eulerian-Lagrangian theory which allows conditioning of the predictions on hydraulic measurements. Conditioning on measured concentrations is also possible, as demonstrated by Neuman et al. (1993). In this paper we condition velocity on log transmissivity and/or hydraulic head data via cokriging. We then combine an early time analytical solution with a pseudo-Fickian Galerkin finite element scheme for later time to obtain conditional predictions of concentration and lower bounds on its variance and coefficient of variation. The pseudo-Fickian scheme involves a conditional dispersion tensor which depends on information and varies in space-time. Hence the predicted plumes travel along curved trajectories and attain irregular, non-Gaussian shapes. We also compute a measure of uncertainty for the original source location of a solute ''particle'' whose position at some later time is known from sampling. Spatial maps of this ''particle origin covariance'' provide vivid images of preferential flow paths and exclusion zones identified by the available data. We illustrate these concepts and results on instantaneous point and area sources. ¿ American Geophysical Union 1995