The geometric configuration of building rooftops considerably influences the lightning leader attachment process. However, observational and modeling studies on how rooftop geometries affect this process remain limited, particularly regarding the combined impacts of building height and lightning peak current on striking distances across diverse rooftop designs. To address this gap, a physics-based lightning strike model for tall buildings was developed based on an established three-dimensional variable grid upward leader initiation model. The model incorporated the attachment process between upward and downward leaders. Four representative rooftop geometries were systematically analyzed: flat-top, sloped roof, cuboid-tower, and cylindrical-tower configurations. The results revealed two critical trends: Qie et al. (2024) (1) Striking distances decrease as rooftop geometries approximate flat-top profiles, whereas rod-like configurations exhibit increased striking distances; Xiao et al. (2023) (2) For sloped roofs, those with a vertex angle exceeding 45° exhibit striking distance characteristics similar to flat-top structures under varying peak currents, whereas steeper slopes behave more like rod-type roofs. Empirical correlations between striking distance (D) and peak current (Ip) are derived for 100 m structures: D = 2.27 × I_P^0.92 (flat-top) and D = 4.29 × I_P^0.80 (rod-type). Furthermore, two universal patterns emerged: (a) Striking distances and upward leader lengths increase proportionally with building height across all geometries; (b) Rooftop geometry exerts a stronger influence on the attachment process at lower peak currents (20 kA), with diminishing effects at higher peak currents (60 kA). These findings provide quantitative guidelines for optimizing lightning protection systems in architecturally complex structures.