The overlap between Autism and Attention-Deficit Hyperactivity Disorder (ADHD) is widely observed in clinical settings, with growing interest in their co-occurrence in neurodiversity research. Until relatively recently, however, concurrent diagnoses of Autism and ADHD were not possible. This has limited the scope for large-scale research on their cross-condition associations, further stymied by a dearth of open science practices in the neurodiversity field. Additionally, almost all previous research linking Autism and ADHD has focused on children and adolescents, despite them being lifelong conditions. Tackling these limitations in previous research, 5504 adults – including a nationally representative sample of the UK (Study 1; n = 504) and a large pre-registered study (Study 2; n = 5000) – completed well-established self-report measures of Autism and ADHD traits. A series of network analyses unpacked the associations between Autism and ADHD at the individual trait level. Low inter-item connectivity was consistently found between conditions, supporting the distinction between Autism and ADHD as separable constructs. Subjective social enjoyment and hyperactivity-impulsivity traits were most condition-specific to Autism and ADHD, respectively. Traits related to attention control showed the greatest Bridge Expected Influence across conditions, revealing a potential transdiagnostic process underlying the overlap between Autism and ADHD. To investigate this further at the cognitive level, participants completed a large, well-powered, and pre-registered study measuring the relative contributions of Autism and ADHD traits to attention control (Study 3; n = 500). We detected age- and sex-related effects, however, attention control did not account for the covariance between Autism and ADHD traits. We situate our findings and discuss future directions in the cognitive science of Autism, ADHD, and neurodiversity, noting how our open datasets may be used in future research.