Numerous brain disorders demonstrate structural brain abnormalities, which are thought to arise from molecular perturbations or connectome miswiring. The unique and shared contributions of these molecular and connectomic vulnerabilities to brain disorders remain unknown, and has yet to be studied in a single multi-disorder framework. Using MRI morphometry from the ENIGMA consortium, we construct maps of cortical abnormalities for thirteen neurodevelopmental, neurological, and psychiatric disorders from N = 21,000 participants and N = 26,000 controls, collected using a harmonised processing protocol. We systematically compare cortical maps to multiple micro-architectural measures, including gene expression, neurotransmitter density, metabolism, and myelination (molecular vulnerability), as well as global connectomic measures including number of connections, centrality, and connection diversity (connectomic vulnerability). We find a relationship between molecular vulnerability and white-matter architecture that drives cortical disorder profiles. Local attributes, particularly neurotransmitter receptor profiles, constitute the best predictors of both disorder-specific cortical morphology and cross-disorder similarity. Finally, we find that cross-disorder abnormalities are consistently subtended by a small subset of network epicentres in bilateral sensory-motor, inferior temporal lobe, precuneus, and superior parietal cortex. Collectively, our results highlight how local molecular attributes and global connectivity jointly shape cross-disorder cortical abnormalities.