The borocarbides RNi2B2C (R=Gd, Ho, Er) exhibit a large variety of magnetic states and as a consequence rich phase diagrams. We have analyzed the nature of these states by specific heat investigations. The data were measured down to 0.5 K and up to 80 kOe. The overall evolution of each Cm(T,H) curve is observed to reflect faithfully the features of the corresponding H-T phase diagram. Within the lower ranges of temperature and fields, the calculations based on linearized field-dependent spin-wave theory are found to reproduce satisfactorily the measured Cm(T,H) curves: accordingly, within these ranges, the thermodynamical properties of these compounds can be rationalized in terms of only two parameters: the spin-wave energy gap and the stiffness coefficient. For the intermediate fields ranges (H1<H<Hsat) wherein successive field-induced metamagnetic modes are stabilized, the evolution of Cm(T,H) is discussed in terms of the Maxwell relation (dCm/dH)T=T(d^2M/dT^2)H. For the particular case of GdNi2B2C wherein the anisotropy is dictated by the classical dipole interaction, Cm(T,H) across the whole ordered state is numerically evaluated within the model of Jensen and Rotter [PRB 77 (2008) 134408].