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Production networks arise from customer–supplier relationships between firms. These systems have gained increasing attention as a consequence of the frequent supply chain disruptions caused by the natural and man-made disasters occurred during the last years (e.g. the Covid-19 pandemic and the Russia-Ukraine war). Recent, empirical evidence has shown that production networks are shaped by 'functional' structures reflecting the complementarity of firms, i.e. their tendency to compete. However, data constraints force the few, available studies to consider only country-specific production networks. In order to fully capture the cross-country structure of modern supply chains, here we focus on the global, automotive industry as depicted by the 'MarkLines Automotive' dataset. After representing it as a network of manufacturers, suppliers and products, we look for the statistical significance of the aforementioned, 'functional' structures. Our exercise reveals the presence of several pairs of manufacturers sharing a significantly large number of suppliers, a result confirming that any two car companies are seldom engaged in a buyer–supplier relationship: rather, they compete although being connected to many, common neighbors. Interestingly, 'generalist' suppliers serving many manufacturers co-exist with 'specialist' suppliers serving few manufacturers. Additionally, we unveil the presence of patterns with a clearly spatial signature, with manufacturers clustering around groups of geographically close suppliers: for instance, Chinese firms constitute a disconnected community, likely an effect of the protectionist policies promoted by the Chinese government. We also show the tendency of suppliers to organize their production by targeting specific car systems, i.e. combinations of technological devices designed for specific tasks. Besides shedding light on the self-organizing principles shaping production networks, our findings open up the possibility of designing realistic generative models of supply chains, to be used for testing the resilience of the global economy. • We study the 'MarkLines' dataset, depicting the automotive industry at the global level. • We organize it as a manufacturer-supplier-product tripartite network. • We perform pattern-detection, employing an entropy-based validation technique. • The self-organization of production networks is driven by complementarity. • Clear geographical patterns emerge, such as the isolation of the Chinese ecosystem. [ABSTRACT FROM AUTHOR]