Attempts to explain the source of r-process elements in nature by particular astrophysical sites face the entwined uncertainties, stemming from the extrapolation of nuclear properties far from stability, inconsistent sources of different properties (e.g., nuclear masses and half-lives), and the (poor) understanding of astrophysical conditions, which are hard to disentangle. We utilize the full isotopic r-process abundances in nature [especially in all of the three peaks (A congruent-to 80, 130, 195)] and a unified model for all nuclear properties involved (aided by recent experimental knowledge in the r-process path), to deduce uniquely the conditions necessary to produce such an abundance pattern. Recent analysis of a few isotopic ratios in the A almost-equal-to 80 and A almost-equal-to 130 r-process peaks led to the conclusion that the r-process abundances originate from a high-density and high-temperature environment, which supports an equilibrium between neutron captures and photodisintegrations. This excludes events where neutrons are released from (alpha, n) reactions in explosive He burning. The present study investigates also the nature of the steady-flow equilibrium of beta decays between isotonic chains. We find strong evidence that a steady flow was not global but only local in between neighboring peaks, which requires time scales not much longer than 1 s. The abundances have to be explained by a superposition of r-process components with varying neutron number densities n(n) > 10(2) cm-3 and temperatures T > 10(9) K, where each of the components proceeds up to one of the peaks. The remaining odd-even effects in observed abundances indicate that neutron densities dropped during freeze-out by orders of magnitude on time scales close to 0.04 s. A set of n(n)-T conditions is presented as a test for any astrophysical r-process site. We also show how remaining deficiencies in the produced abundance pattern can be used to extract nuclear properties far from stability.