A method is outlined to vary reproducibly the density of [111] P(b) centers (.Si = Si3 defects with an unpaired sp3 orbital perpendicular to the interface) at the thermal (111)Si/SiO2 interface (grown at almost-equal-to 920-degrees-C; 1.1 atm O2) using alternate non-in situ H passivation (hydrogenation in pure H-2 at temperatures T = 253-degrees-C-353-degrees-C) and degassing (high vacuum of p < 10(-6) Torr at T = 752-degrees-C-835-degrees-C). These soft thermal treatments may be randomly sequenced and do not affect the interface structure. Only the spin state (electron spin resonance activity) of P(b) centers is modified by bonding or releasing H. The total number of .Si = Si3 defects-either passivated or not-remains unaltered and seems to be set by the initial oxidation step. The maximum P(b) density is about 1.5% of the Si atom sites in a (111) plane, which appears as a natural constant for the (111)Si/SiO2 interface thermally grown at almost-equal-to 920-degrees-C. This [P(b)] monitoring is used as a tool to unveil the dipole-dipole (DD) influence on the K-band electron-spin-resonance spectrum of P(b) centers. The main effects are an overall broadening of the Zeeman resonance and the appearance of fine-structure doublets that grow with increasing concentration. Measurements at low P(b) concentrations reveal the residual dangling-bond resonance (void of dipolar interactions). Simulation of this signal using theoretical hyperfine parameters predicted from a relaxed Si22H27 P(b) model cluster shows these to be somewhat underestimated. For higher P(b) concentrations, dipolar spectra were calculated, starting from a supposed array of possible P(b) sites in a (111)Si plane over which the P(b) centers are randomly distributed, by exact diagonalization of the spin Hamiltonian for a large number of possible configurations over the array. These are compared with experiments to derive the spatial distribution of the P(b) centers. Several site arrays were tested, leading to strong evidence that the P(b) centers are randomly distributed over all Si atom sites at the interfacial terraces. Models incorporating a strong clustering of P(b) centers or correlating them with interfacial steps are excluded. Also, the ditrigonal ring P(b) silica-cap model appears inappropriate. Fine structure due to first-, second-, third-, and fourth-neighbor interactions are not observed. This is ascribed to superexchange interaction between neighboring spins; the magnitude of exchange is shown to be compatible with previous observations on other Si dangling-bond-like defects in bulk Si. The superhyperfine structure (of splitting A parallel-to shf = 14.8 +/- 0.2 G) due to P(b)-electron interactions with Si-29 nuclei at second-nearest-neighbor positions in the Si substrate, has conclusively been distinguished from the DD fine structure. Previous investigations of the DD interactions are consistently explained resulting in a consistent picture of the two-dimensional P(b) system as regards dipolar and hyperfine interactions, saturation behavior, and moment calculations.