Traditional industrial recommenders are usually trained on a single business domain and then serve for this domain. However, in large commercial platforms, it is often the case that the recommenders need to make click-through rate (CTR) predictions for multiple business domains. Different domains have overlapping user groups and items. Thus, there exist commonalities. Since the specific user groups have disparity and the user behaviors may change in various business domains, there also have distinctions. The distinctions result in domain-specific data distributions, making it hard for a single shared model to work well on all domains. To learn an effective and efficient CTR model to handle multiple domains simultaneously, we present Star Topology Adaptive Recommender (STAR). Concretely, STAR has the star topology, which consists of the shared centered parameters and domain-specific parameters. The shared parameters are applied to learn commonalities of all domains, and the domain-specific parameters capture domain distinction for more refined prediction. Given requests from different business domains, STAR can adapt its parameters conditioned on the domain characteristics. The experimental result from production data validates the superiority of the proposed STAR model. Since 2020, STAR has been deployed in the display advertising system of Alibaba, obtaining averaging 8.0% improvement on CTR and 6.0% on RPM (Revenue Per Mille).