Structure of the decay _ B0s. J=.p_p- is studied using data corresponding to 3 fb- 1 of integrated luminosity from pp collisions produced by the LHC and collected by the LHCb detector. Five interfering p_p- states are required to describe the decay: F-0(980), F-0(1500), F-0(1790), F-2 (1270) and F-2(1525) An alternative model including these states and a nonresonant J=.p_p- component also provides a good description of the data. Based on the different transversity components measured for the spin- 2 intermediate states, the final state is found to be compatible with being entirely CP odd. The CP- even part is found to be < 2.3% at a 95% confidence level. The f 0d500_ state is not observed, allowing a limit to be set on the absolute value of the mixing angle with the f 0d980_ of < 7.7 at a 90% confidence level, consistent with a tetraquark interpretation of the f(0)(980) substructure.