Ethylene polymerization using a catalyst derived from the reaction of the phosphorane (Me3Si)(2)NP(NSiMe3)(2) (1) with either Ni(COD)(2) or bis(pi-allyl)Ni complexes affords branched poly(ethylene) (PE) of variable MW (10(3)-10(6)) depending on conditions. The branched PE of high MW is semicrystalline with T-m < 100 degrees C. High field C-13 NMR spectra reveal the presence of methyl branches (ca. 10-15 per 1000 C atoms), branches longer than six C atoms (15-20 per 1000 C atoms) and trace levels of ethyl, propyl, n-butyl, and sec-butyl branches (total < 2 per 1000 C atoms). The branching distribution changes modestly in response to changes in ethylene pressure in a manner consistent with a chain-walking mechanism. Analysis of high MW polymers by GPC-light scattering reveals the presence of sparse long-chain branching (g(M) = 0.78-0.93 with < 1 long-chain branch per molecule); the branched PE formed is thus similar to low-density PE. Addition of alpha-olefin during polymerization leads to enhanced activity but is accompanied by chain transfer. The only evidence of alpha-olefin incorporation is at the chain-ends in the case of 4-methylpentene, and there is little change to the branching distribution in the presence of alpha-olefin. A sterically hindered nickel iminophosphonamide (PN2) complex (Me3Si)(2)NP(Me)(NSiMe3)(2)NiPh(PPh3) (2) was prepared and characterized by X-ray crystallography. This complex oligomerizes ethylene to branched material with a microstructure very similar to that observed using the catalysts derived from phosphorane 1 and Ni(COD)(2) or (pi-allyl)(2)Ni. DFT modeling of the active catalyst, coupled with stochastic simulation of chain growth, reveals that a chain-walking vs insertion mechanism can account for the short-chain branching distributions observed. Kinetic modeling of the observed branching distribution can account for relative intensity of the short branches (<= C-5) as well as those of the longer branches. However, in order to fit the intensity of the Hx(+) branches, one of the key parameters in the model, the probability of chain-walking for higher secondary Ni-R groups, converges to a value similar to 1. This finding is not anticipated by the DFT results and suggests that the longer branches present in these materials do not form by a chain-walking vs insertion mechanism.