  We study how codimension-two objects like vortices back-react gravitationally
with their environment in theories (such as 4D or higher-dimensional
supergravity) where the bulk is described by a dilaton-Maxwell-Einstein system.
We do so both in the full theory, for which the vortex is an explicit classical
`fat brane' solution, and in the effective theory of `point branes' appropriate
when the vortices are much smaller than the scales of interest for their
back-reaction (such as the transverse Kaluza-Klein scale). We extend the
standard Nambu-Goto description to include the physics of flux-localization
wherein the ambient flux of the external Maxwell field becomes partially
localized to the vortex, generalizing the results of a companion paper to
include dilaton-dependence for the tension and localized flux. In the effective
theory, such flux-localization is described by the next-to-leading effective
interaction, and the boundary conditions to which it gives rise are known to
play an important role in how (and whether) the vortex causes supersymmetry to
break in the bulk. We track how both tension and localized flux determine the
curvature of the space-filling dimensions. Our calculations provide the tools
required for computing how scale-breaking vortex interactions can stabilize the
extra-dimensional size by lifting the dilaton's flat direction. For small
vortices we derive a simple relation between the near-vortex boundary
conditions of bulk fields as a function of the tension and localized flux in
the vortex action that provides the most efficient means for calculating how
physical vortices mutually interact without requiring a complete construction
of their internal structure. In passing we show why a common procedure for
doing so using a $\delta$-function can lead to incorrect results. Our
procedures generalize straightforwardly to general co-dimension objects.
