Abstract Several aspects of the internal structure of pseudoscalar mesons, accessible through generalized parton distributions in their zero-skewness limit, are examined. These include electromagnetic and gravitational form factors related to charge and mass densities; and distributions in the impact parameter space. To this end, we employ an algebraically viable framework that is based upon the valence-quark generalized parton distribution expressed explicitly in terms of the associated distribution function and a profile function that governs the off-forward dynamics. The predominantly analytical nature of this scheme yields several algebraic results and relations while also facilitating the exploration of insightful limiting cases. With a suitable input distribution function, guided either by experiment or theory, and with an appropriate choice of the profile function, it is possible to provide testable predictions for spatial distributions of valence quarks inside pseudoscalar mesons. When comparison is possible, these predictions align well with existing experimental data as well as the findings of reliable theoretical approaches and lattice QCD.