In this paper the problem of recovering the temporal release history of a pollutant is approached with a geostatistical methodology that analyzes the pollutant concentration measured at a given time in the aquifer. The adopted methodology was developed by Snodgrass and Kitanidis <1997> for one-dimensional flow and transport. Here it is extended to the case of two-dimensional transport and additional improvements are carried out, with important consequences on technical applications. A literature numerical case study is used to assess the quality of the results and the performance of the algorithms with regard to (1) the plume sampling scheme, (2) the impact of concentration measurement errors, (3) the impact of errors on the estimated aquifer parameters, and (4) the erroneous identification of the hydraulic gradient direction. The new applications focus on the incorporation of nonpoint and multiple sources in order to quantify the relative legal liability of the different sources. The results of the numerical analysis show that the method provides a reasonable description of the release history and associated estimate error variance.