We analysed the parsec-scale linear polarization properties of 436 active galactic nuclei (AGNs) based on 15 GHz polarimetric Very Long Baseline Array observations. We present polarization and total intensity images averaged over at least five epochs since 1996 January 19 through 2019 August 4. Stacking improves the image sensitivity down to ∼30 μJy beam−1 and effectively fills out the jet cross-section both in total intensity and linear polarization. It delineates the long-term persistent magnetic field configuration and its regularity by restoring spatial distributions of the electric vector position angle (EVPA) and fractional polarization, respectively. On average, about 10 yr of stacking period is needed to reveal the stable and most-complete polarization distribution of a source. We find that the degree of polarization significantly increases down and across the jet towards its edges, typically manifesting U or W-shaped transverse profiles, suggesting a presence of a large-scale helical magnetic field associated with the outflow. In some AGN jets, mainly BL Lacs, we detect quasi-constant fractional polarization profiles across the jet, accompanied by EVPAs that closely follow the outflow. BL Lacs show higher fractional polarization values in their cores and jets than those in quasars up to hectoparsec de-projected scales, while on larger scales, they become comparable. High-synchrotron-peaked BL Lac jets are found to be less polarized than intermediate and low-synchrotron-peaked BL Lacs. The spatial distribution of the EVPAs in BL Lacs tend to align with the local jet direction, while quasars show an excess of orthogonal polarization orientation.