The recently introduced end-bridging (EB) Monte Carlo move is revisited, and a thorough analysis of its geometric formulation and numerical implementation is given. Detailed results are presented from applying the move, along with concerted rotation, in atomistic simulations of polyethylene (PE) melt systems with mean molecular lengths ranging from C-78 up to C-500, flat molecular weight distributions, and polydispersity indices I ranging from 1.02 to 1.12. To avoid finite system-size effects, most simulations are executed in a superbox containing up to 5000 mers and special neighbor list strategies are implemented. For all chain lengths considered, excellent equilibration is observed of the thermodynamic and conformational properties of the melt at all length scales, from the level of the bond length to the level of the chain end-to-end vector. In sharp contrast, if no end bridging is allowed among the Monte Carlo moves, no equilibration is achieved, even for the C-78 system. The polydispersity index I is found to have no effect on the equilibrium properties of the melt. To quantify the efficiency of the EB Monte Carlo move, the CPU time to required for the chain center of mass to travel a distance equal to the root-mean-square end-to-end distance is estimated by simple analytical arguments. It is found that to should scale as n/((X) over bar Delta(2.5)), where n is the total number of mers in the system, (X) over bar is the average chain length, and Delta similar or equal to [3(I - 1)](1/2) is the reduced width of the chain-length distribution function. This means that, if the size of the model system and the shape of the chain-length distribution are kept constant, systems of larger average molecular weight equilibrate faster, a remarkable attribute of the EB Monte Carlo method. The simulation results obey the estimated scaling of t(0) with (X) over bar, n, and Delta remarkably well in the range of chain lengths and polydispersities for which the premises of the analysis are not violated (mean chain lengths greater than C-156 and polydispersity indices above about 1.07). Results for volumetric behavior, structure, and chain conformation at temperature T = 450 K and pressure P ranging from 1 to 800 atm are presented, using three different PE united atom models proposed in the recent literature. All three models are shown to overestimate the density by ca. 4% and also overestimate the stiffness of chains. The Yoon et al. model is in best agreement with experimental characteristic ratios. Simulation predictions for the structure factor and for the chain-length dependence of the density are in excellent agreement with experiment.