The existing research lacks attention to the borrowed size of cities in urban agglomerations. To fill this research gap, this study examined the existence, spatial conditions, and formation mechanism of borrowed size in 14 urban agglomerations of China from the dimensions of function and performance based on the data of cities above prefecture level in 2008-2019. The results show that: 1) Cities in seven urban agglomerations, namely, Chang-Zhu-Tan, Pearl River Delta, Wuhan, Central and Southern Liaoning, Harbin and Changchun, Beibu Gulf, and Beijing-Tianjin-Hebei regions, have borrowed size. Large cities are more likely to borrow function and borrow performance, that is, there is borrowed size, while small and medium cities are more likely to borrow function. Five urban agglomerations, namely, Chengdu-Chongqing, Central Plains, Shandong Peninsula, Guangdong-Fujian-Zhejiang Coast, and Yangtze River Delta regions, have agglomeration shadow. 2) Borrowed size occurs more frequently in urban agglomerations with polycentric structure. Large, medium, and small cities can borrow function by being embedded into urban agglomerations of polycentric structure, but only medium and large cities can borrow performance in urban agglomerations of polycentric structure. Polycentric structure has the most obvious impact on the borrowed function and borrowed performance of medium cities. 3) Enhancing the geographical proximity of cities will reduce the borrowed function, but can improve the borrowed performance. Enhancing the network relevance of cities can improve the borrowed function and borrowed performance. For borrowed function, there is a substitution effect between network relevance and geographical proximity, and for borrowed performance, there is a complementary effect between network relevance and geographical proximity. The stimulation of network relevance on borrowed function and borrowed performance can only be seen in large cities.
