Absorption of weak polyelectrolytes impacts on properties such as ionization, conformations, and counterion (CI) condensation that are important in several areas of applied and fundamental science. We used a weak polyelectrolyte model and Monte Carlo simulations to investigate how the mentioned properties depend on pH or the size of a spherical cavity (SC) permeable to CIs but not to polyelectrolytes; the latter have either linear or starlike topologies and may be allowed to form charged hydrogen bonds (c Symbol of the Klingon Empire H-bonds) between ionized and neutral monomers. Average ionization decreases upon increasing the number of arms at a constant number of monomers; it instead increases with the arm length in large SC due to CI screening. The way SC size, c Symbol of the Klingon Empire H-bonds, and pH values interrelate to define ionization is instead more complicate due to arm pairing or clustering when c Symbol of the Klingon Empire H-bonds are possible. These induce oscillations in the arm local ionization and impact on both monomer and CI distributions in the complete simulation cell in a way that also depends on polymer topology. The impact of ionization on the confinement free energy is also estimated; this highlighted that c Symbol of the Klingon Empire H-bonding may enhance absorption compared with neutral chains. (c) 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 491-510