We report molecular dynamics simulations on the phase separation of "perfectly mixed" water/oil/tri-n-butylphosphate (TBP) solutions containing 30 or 60 TBP molecules and 5 UO(2)(NO(3))(2) complexes. The oil phase is mimicked by one of two liquids, either chloroform or supercritical CO(2) (SC-CO(2)). The simulations demonstrate the importance of TBP concentration. In the TBP(30) systems, the water and oil phases separate on the nanosecond time scale, leading to two interfaces onto which all TBPs adsord. Some of them spontaneously form 1:1 and 1:2 complexes with UO(2)(NO(3))(2) at the interface. With the more concentrated TBP(60) systems, water and oil do not separate but form microemulsions containing neat water "droplets" surrounded by oil in which TBP is solubilized, sitting at the oil-water boundaries delimiting the droplets. All UO(2)(NO(3))(2) salts are complexed by TBP at the liquid boundaries, sitting somewhat more in oil than in water. Following the Le Chatelier rule, the proportion of 1:2 complexes is larger in the TBP60 system than in the TBP(30) system. Thus, TBP acts not only as a complexant but also as an "interface modifier". The simulations reveal strong analogies between chloroform and SC-CO(2) as organic phases. These novel results are crucial for our understanding of the state of heterogeneous solutions involved in uranyl extraction by TBP as well as assisted cation extraction by other extractants.