The high resolution phase diagram of the tetramethylammonium heptadecafluorononanoate (TMAHFN)/D2O system has been mapped out using H-2 and N-14 NMR spectroscopy. The N-14 quadruple splittings are more than an order of magnitude larger than corresponding H-2 splittings, while the line widths are only two to three times larger. Thus, N-14 NMR offers an order of magnitude improvement over H-2 NMR in the resolution of the spectra from coexisting phases. The H-2 spectra of samples in biphasic regions are often complicated by chemical exchange of D2O molecules between coexisting phases, particularly at low TMAHFN concentrations. Analysis of the H-2 line shapes of a TMAHFN/D2O sample with a weight fraction of TMAHFN of 0.230 obtained at various times following cooling of the sample into the isotropic/nematic biphasic region shows that the mean diameter for the dispersed nematic droplet grows from about 7 to about 26 mum over a period of 2 h. At a mean droplet size of 7 mum the exchange of TMA+ ions between the coexisting phases is slow on the NMR time-scale and exchange effects are not observed in N-14 spectra. The TMAHFN/D2O phase diagram exhibits the generic form of those of the CsPFO/water and APFO/D2O systems, which are the only other systems composed of stable discotic micelles for which high resolution phase diagrams are currently available, but the nematic phase is displaced to smaller TMAHFN concentrations. Specifically, a discotic nematic phase N(D)+, intermediate between an isotropic micellar phase I and a lamellar phase L, exists for weight fractions of TMAHFN between 0.149 (theta = 0.105) and 0.420 (theta = 0.325) and temperatures between 277.3 and 327.6K.