Background: Writing involves multiple processes, drawing on a number of language, cognitive, and print-related skills, and knowledge. According to the Direct and Indirect Effects model of Writing (DIEW; Kim & Park, 2019, "Reading and Writing," 32, 1319), these multiple factors have hierarchical, interactive, and dynamic relations. Aims: I examined the hierarchical relations of language and cognitive skills to written composition as well as the relation of topic knowledge to written composition, using DIEW as a theoretical framework. Sample: One hundred thirty-two English-speaking students in Grade 4 were assessed on written composition, topic knowledge, oral language (vocabulary, grammatical knowledge, discourse-level oral production), higher order cognitions (inference, perspective taking [theory of mind], monitoring), domain-general cognitions (working memory and attention), and transcription skills (spelling and handwriting fluency). Methods: Structural equation modelling was used to compare hierarchical relations models with a direct or flat relations model. Results: The hierarchical relations model was supported. Discourse oral language skills and transcription skills completely mediated the relations of the other component skills to written composition, and the included component skills explained 82% of variance in written composition. Substantial total effects were found for discourse language, transcription, attention, working memory, vocabulary, theory of mind, and grammatical knowledge. Topic knowledge was moderately related to writing, but this relation became weak once the other skills were accounted for. Conclusions: Component skills have hierarchical structural relations and make direct and indirect contributions to written composition. Furthermore, the role of topic knowledge in written composition appears constrained by language and transcription skills for developing writers. [For the corresponding grantee submission, see ED602708.]