  A symmetry-preserving approach to the two valence-body continuum bound-state
problem is used to calculate the elastic electromagnetic form factors of the
$\rho$-meson and subsequently to study the evolution of vector-meson form
factors with current-quark mass. To facilitate a range of additional
comparisons, $K^\ast$ form factors are also computed. The analysis reveals
that: vector mesons are larger than pseudoscalar mesons; composite vector
mesons are non-spherical, with magnetic and quadrupole moments that deviate
$\sim 30$\% from point-particle values; in many ways, vector-meson properties
are as much influenced by emergent mass as those of pseudoscalars; and vector
meson electric form factors possess a zero at spacelike momentum transfer.
Qualitative similarities between the electric form factors of the $\rho$ and
the proton, $G_E^p$, are used to argue that the character of emergent mass in
the Standard Model can force a zero in $G_E^p$. Morover, the existence of a
zero in vector meson electric form factors entails that a single-pole vector
meson dominance model can only be of limited use in estimating properties of
off-shell vector mesons, providing poor guidance for systems in which the
Higgs-mechanism of mass generation is dominant.
