In order to describe the isonymic structure of Paraguay, the distribution of 4,843,868 surnames of 2,882,163 persons was studied in the 18 departments and 237 districts of the nation. The correlations between isonymic and geographic distances for departments were r = 0.713 ± 0.052 for Euclidean distance, 0.597 ± 0.074 for Nei's and 0.582 ± 0.076 for Lasker's, and for districts r = 0.320 ± 0.007, 0.235 ± 0.009 and 0.422 ± 0.008, respectively. Average α was 151 for the entire country, 140.6 ± 6.5 for departments and 108.2 ± 2.7 for districts. The geographical distribution of districts'α is compatible with the settlement of subsequent groups of migrants moving from South towards the Centre and North of Paraguay. The geographical analysis of the first three components of Lasker's isonymy distance matrix is in agreement with such a process. The prevalence of Spanish-Amerindian ethnic groups and the relative absence of indigenous surnames (absence due mainly to the forced surname change of 1848) is in agreement with the diffusion of Spanish speaking males over a low-density area populated by indigenous groups. The present distribution of Y-markers and mt-markers in the available studies in most Latin American populations is compatible with this process.