Re-creating the observed diversity in the organization of baryonic mass within dark matter haloes represents a key challenge for galaxy formation models. To address the growth of galaxy discs in dark matter haloes, we have constrained the distribution of baryonic and non-baryonic matter in a statistically representative sample of 44 nearby galaxies defined from the Extended Disk Galaxy Exploration Science (EDGES) Survey. The gravitational potentials of each galaxy are traced using rotation curves derived from new and archival radio synthesis observations of neutral hydrogen (H I). The measured rotation curves are decomposed into baryonic and dark matter halo components using 3.6 μ m images for the stellar content, the H I observations for the atomic gas component, and, when available, CO data from the literature for the molecular gas component. The H I kinematics are supplemented with optical integral field spectroscopic (IFS) observations to measure the central ionized gas kinematics in 26 galaxies, including 13 galaxies that are presented for the first time in this paper. Distributions of baryonic-to-total mass ratios are determined from the rotation curve decompositions under different assumptions about the contribution of the stellar component and are compared to global and radial properties of the dominant stellar populations extracted from optical and near-infrared photometry. Galaxies are grouped into clusters of similar baryonic-to-total mass distributions to examine whether they also exhibit similar star and gas properties. The radial distribution of baryonic-to-total mass in a galaxy does not appear to correlate with any characteristics of its star formation history.