A commercial low-density polyethylene copolymer, poly(ethylene-co-vinyl acetate) (EVA), synthesized via the high-pressure free-radical polymerization process, was fractionated with supercritical propylene by isothermal increasing pressure profiling and critical, isobaric, temperature rising elution fractionation (CITREF(TM)). Extensive characterization of the fractions by nuclear magnetic resonance (NMR) spectroscopy, gel permeation chromatography (GPC) in combination with low-angle laser light scattering (LALLS), and differential scanning calorimetry (DSC) was used to map not only the molecular-weight and chemical composition distributions of the parent copolymer, but also its short-chain branch (SCB) and long-chain branch (LCB) distributions. Fractionation by increasing pressure profiling confirmed the broad molecular-weight distribution and the narrow acetate-branch distribution expected for this random copolymer but revealed the presence of a small amount (similar to 2 wt%) of low molecular-weight amorphous species containing a high level of alkyl SCBs (80 branches/1000 C). The LCB density estimated from the Zimm-Stockmayer relationship using the GPC data monotonically increases with increasing molecular weight above 60,000 g/mol, in agreement with the kinetics of free-radical polymerization. CITREF(TM) was found to fractionate this copolymer by crystallinity, which is influenced by both the alkyl SCBs and the acetate branches. Up to 18% difference in total branch density (<5% in crystallinity) between EVA molecules was identified using CITREF(TM).