  We show here that population growth, resolved at the county level, is
spatially heterogeneous both among and within the U.S. metropolitan statistical
areas. Our analysis of data for over 3,100 U.S. counties reveals that annual
population flows, resulting from domestic migration during the 2015 - 2019
period, are much larger than natural demographic growth, and are primarily
responsible for this heterogeneous growth. More precisely, we show that
intra-city flows are generally along a negative population density gradient,
while inter-city flows are concentrated in high-density core areas. Intra-city
flows are anisotropic and generally directed towards external counties of
cities, driving asymmetrical urban sprawl. Such domestic migration dynamics are
also responsible for tempering local population shocks by redistributing
inflows within a given city. This "spill-over" effect leads to a smoother
population dynamics at the county level, in contrast to that observed at the
city level. Understanding the spatial structure of domestic migration flows is
a key ingredient for analyzing their drivers and consequences, thus
representing a crucial knowledge for urban policy makers and planners.
