Abstract: The Z(c)(+/-)(3900)/Z(c)(+/-)(3885) resonant structure has been experimentally observed in the Y(4260) -> J/Psi pi pi and Y(4260) -> (D) over bar* D pi decays. This structure is intriguing since it is a prominent candidate of an exotic hadron. Yet, its nature is unclear so far. In this work, we simultaneously describe the (D) over bar* D and J/Psi pi invariant mass distributions in which the Z(c) peak is seen using amplitudes with exact unitarity. Two different scenarios are statistically acceptable, where the origin of the Z(c) state is different. They correspond to using energy dependent or independent (D) over bar *D S-wave interaction. In the first one, the Z(c) peak is due to a resonance with a mass around the D (D) over bar* threshold. In the second one, the Z(c) peak is produced by a virtual state which must have a hadronic molecular nature. In both cases the two observations, Z(c)(+/-)(3900) and Z(c)(+/-)(3885), are shown to have the same common origin, and a (D) over bar *D bound state solution is not allowed. Precise measurements of the line shapes around the D (D) over bar* threshold are called for in order to understand the nature of this state.