High-precision oxygen isotopic compositions of eighteen large cosmic spherules (> 500 mu m diameter) from the Atacama Desert, Chile, were determined using IR-laser fluorination - Isotope Ratio Mass spectrometry. The four discrete isotopic groups defined in a previous study on cosmic spherules from the Transantarctic Mountains (Suavet et al., 2010) were identified, confirming their global distribution. Approximately 50% of the studied cosmic spherules are related to carbonaceous chondrites, 38% to ordinary chondrites and 12% to unknown parent bodies. Approximately 90% of barred olivine (BO) cosmic spherules show oxygen isotopic compositions suggesting they are related to carbonaceous chondrites. Similarly, similar to 90% porphyritic olivine (Po) cosmic spherules are related to ordinary chondrites and none can be unambiguously related to carbonaceous chondrites. Other textures are related to all potential parent bodies. The data suggests that the textures of cosmic spherules are mainly controlled by the nature of the precursor rather than by the atmospheric entry parameters. We propose that the Po texture may essentially be formed from a coarse-grained precursor having an ordinary chondritic mineralogy and chemistry. Coarse-grained precursors related to carbonaceous chondrites (i.e. chondrules) are likely to either survive atmospheric entry heating or form V-type cosmic spherules. Due to the limited number of submicron nucleation sites after total melting, ordinary chondrite-related coarse-grained precursors that suffer higher peak temperatures will preferentially form cryptocrystalline (Cc) textures instead of BO textures. Conversely, the BO textures would be mostly related to the fine-grained matrices of carbonaceous chondrites due to the wide range of melting temperatures of their constituent mineral phases, allowing the preservation of submicron nucleation sites. Independently of the nature of the precursors, increasing peak temperatures form glassy textures.