Urban growth has evolved from cities to metropolitan areas and urban agglomerations, exhibiting a multi-scale pattern. Urban scaling law can reflect the nonlinear relationship between urban indicators and population size, which is very important for urban planning through analyzing the evolution of urban system characteristics. However, existing studies mainly focused on scalar law within countries, neglecting the multi-scale synergistic evolution of complex urban systems. The purpose of this study is to investigate the scalar relationship between urban indicators and population size at multiple scales from the perspective of individual cities, metropolitan areas, and urban agglomerations, using data from 45 cities in three urban agglomerations in eastern China. Based on the urban scaling law, local spatial autocorrelation model is used to analyze and explore the collaborative evolution of multiple scales. Results show that from the perspective of time evolution, the three urban agglomerations exhibit greater scaling effects than metropolitan areas, with a scaling exponent (β) greater than 1 for urban indicators including economy, land, infrastructure, ecological pressure, and innovation. From the perspective of spatial differences, the spatial development gap between the metropolitan area scale and the urban agglomeration scale is relatively small compared with the city scale. In addition, the Beijing–Tianjin–Hebei urban agglomeration (BTH) mainly displays the synergistic development of the dual-core structure of Beijing and Tianjin. The Yangtze River Delta (YRD) exhibits significant disparities between its cities, resulting in a low degree of overall synergy. In contrast, the Guangdong-Hong Kong-Macao Greater Bay Area (GBA) leads in terms of synergistic evolution. This study is crucial to help understand the development of urban systems at different scales and to support regional planning and the achievement of coordinated development.

The digital economy has become an important force driving regional transformation and green development, yet existing evidence on its net carbon-balance effects on land-use carbon emission efficiency (LUCEE) remains limited. Using panel data for 41 cities in the Yangtze River Delta from 2002 to 2022, this study first calculates city-level net carbon-emission pressure by jointly considering anthropogenic carbon emissions and land-based carbon sequestration, and then evaluates LUCEE using a super-efficiency SBM model with undesirable outputs, in which urban construction land is incorporated as an independent input rather than used as a common scaling denominator. A two-way fixed-effects model, mediation model, geographical detector, and spatial econometric model are further employed to examine the temporal dynamics, transmission mechanisms, spatial heterogeneity, and spatial associations of the digital economy. This study finds that, in the short term, digital-economy development is significantly negatively associated with LUCEE, while this negative association gradually weakens over time, with no clear evidence of a positive reversal within the observed lag structure. Industrial tertiarisation shows partial and limited evidence as a transmission channel, although it does not automatically translate into greener land-use performance. The digital economy also helps explain LUCEE heterogeneity and shows enhanced explanatory power when combined with government intervention, land-use intensity, industrial tertiarisation, and economic development. Moreover, the spatial analysis provides supplementary evidence of a negative association between digital-economy development in spatially connected cities and local LUCEE, although this finding should be interpreted cautiously given the limited evidence of endogenous spatial dependence. These findings deepen the understanding of the low-carbon consequences of digitalisation and provide policy implications for green digital development, industrial transformation, and regionally coordinated carbon mitigation.