A comprehensive n.m.r. characterization of a low-density polyethylene (LDPE) sample with respect to the distribution of short branches, saturated and unsaturated long branch/chain ends is presented. High precision carbon chemical shift values of all assigned resonance peaks with standard deviations of less than 0.005ppm (at 403K and 75MHz carbon resonance frequency) were obtained by mathematical deconvolution of the carbon spectrum, thus enabling a differentiation not only of short branches (C-n<6) but also hexyl-, oxtyl- and longer branches). Nuclear Overhauser Enhancement (NOE) measurements revealed that less than 50% of the non-equivalent carbon nuclei experienced full NOE of 2.98 while more than 25% of the corresponding carbon nuclei showed a NOE of less than 2.75. Based on spin-lattice relaxation time (T-1) and NOE measurements a statistical evaluation showed that internal quantitative consistency between peak intensities existed only under no-NOE conditions. Derived branch distribution numbers from a set of 100 synthetic carbon n.m.r. spectra of the sample, revealed that each branch could be characterized by a Gaussian or normal distribution function. Average values and standard deviations of the branch numbers are presented.