Psychiatric conditions in parents are associated with many psychiatric and nonpsychiatric outcomes in offspring. However, it remains unknown whether this intergenerational transmission is attributable to broader psychopathology comorbidity or to specific conditions. To estimate associations between general and specific psychopathology factors in parents and a wide range of register-based outcomes in their offspring. This Swedish national register-based cohort study included 2 947 703 individuals born between 1970 and 2000 and followed up with participants through December 31, 2013. Statistical analysis was performed from October 2022 to October 2023. Hierarchical factor model consisting of 1 general and 3 specific psychopathology factors fit to 9 parental psychiatric diagnoses and violent criminal court convictions. A total of 31 outcomes were measured in offspring and sorted into 6 broad clusters: psychotic-like outcomes, neurodevelopmental outcomes, internalizing outcomes, externalizing outcomes, behavior and accidents, and psychosocial outcomes. Of 2 947 703 individuals, 1 518 252 (51.5%) were male, and the mean (SD) age at the end of follow-up was 28.7 (8.9) years. The general psychopathology factor in parents was significantly associated with all 31 offspring outcomes (range: odds ratio [OR] for accidents, 1.08 [95% CI, 1.07-1.08] to OR for social welfare recipiency, 1.40 [95% CI, 1.39-1.40]), which means that children whose parents scored 1 SD above the mean on the general psychopathology factor had an 8% to 40% higher odds of different studied outcomes. The specific psychotic factor in parents was primarily associated with all 5 psychotic-like outcomes (range: OR for prescription of antiepileptics, 1.05 [95% CI, 1.04-1.06] to OR for schizophrenia, 1.25 [95% CI, 1.23-1.28]) and the specific internalizing factor in parents was primarily associated with all 6 internalizing outcomes (range: OR for prescription of anxiolytics, 1.10 [95% CI, 1.09-1.10] to OR for depression, 1.13 [95% CI, 1.12-1.13]) and all 6 neurodevelopmental outcomes (range: OR for intellectual disability, 1.02 [95% CI, 1.01-1.03] to OR for autism spectrum disorder, 1.10 [95% CI, 1.09-1.11]) in offspring. The specific externalizing factor in parents was associated with all 6 externalizing outcomes (range: OR for violent crimes, 1.21 [95% CI, 1.19-1.23] to OR for oppositional defiant disorder, 1.32 [95% CI, 1.32-1.33]) and all 6 internalizing outcomes (range: OR for obsessive-compulsive disorder, 1.01 [95% CI, 1.00-1.02] to OR for posttraumatic stress disorder, 1.13 [95% CI, 1.12-1.13]) in offspring. This cohort study of the Swedish population suggests that the intergenerational transmission of psychiatric conditions across different types of spectra may largely be attributable to a parental general psychopathology factor, whereas specific factors appeared to be primarily responsible for within-spectrum associations between parents and their offspring. Professionals who work with children (eg, child psychologists, psychiatrists, teachers, and social workers) might benefit from taking the total number of parental psychiatric conditions into account, regardless of type, when forecasting child mental health and social functions.