In recent years, several models have improved the capacity to generate synthetic tabular datasets. However, such models focus on synthesizing simple columnar tables and are not useable on real-life data with complex structures. This paper puts forward a generic framework to synthesize more complex data structures with composite and nested types. It then proposes one practical implementation, built with causal transformers, for struct (mappings of types) and lists (repeated instances of a type). The results on standard benchmark datasets show that such implementation consistently outperforms current state-of-the-art models both in terms of machine learning utility and statistical similarity. Moreover, it shows very strong results on two complex hierarchical datasets with multiple nesting and sparse data, that were previously out of reach.