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Understanding scaling relations of social and environmental attributes of urban systems is necessary for effectively managing cities. Urban scaling theory (UST) has assumed that population density scales positively with city size. We present a new global analysis using a publicly available database of 933 cities from 38 countries. Our results showed that (18/38) 47% of countries analyzed supported increasing density scaling (pop ~ area) with exponents ~⅚ as UST predicts. In contrast, 17 of 38 countries (~45%) exhibited density scalings statistically indistinguishable from constant population densities across cities of varying sizes. These results were generally consistent in years spanning four decades from 1975 to 2015. Importantly, density varies by an order of magnitude between regions and countries and decreases in more developed economies. Our results (i) point to how economic and regional differences may affect the scaling of density with city size and (ii) show how understanding country- and region-specific strategies could inform effective management of urban systems for biodiversity, public health, conservation and resiliency from local to global scales.200 word statement of contribution: Urban Scaling Theory (UST) is a general scaling framework that makes quantitative predictions for how many urban attributes spanning physical, biological and social dimensions scale with city size; thus, UST has great implications in guiding future city developments. A major assumption of UST is that larger cities become denser. We evaluated this assumption using a publicly available global dataset of 933 cities in 38 countries. Our scaling analysis of population size and area of cities revealed that while many countries analyzed showed increasing densities with city size, about 45% of countries showed constant densities across cities. These results question a key assumption of UST. Our results suggest policies and management strategies for biodiversity conservation, public health and sustainability of urban systems may need to be tailored to national and regional scaling relations to be effective.