  We investigate saturation effects in $ep$ scattering as well as in
ultraperipheral $p$A and AA collisions at small $x$ with four variants of the
impact parameter dependent color dipole model: with and without gluon
saturation and with and without a novel mechanism that suppresses unphysical
dipole radii above the confinement scale, a problem not addressed by most
implementations. We show that $ep$ scattering at HERA can be very well
described by any of the four variants. When going from $ep$ to $e$A scattering,
saturation effects are expected to increase as $\sim$A$^{1/3}$. In lieu of an
electron-ion collider, we confront the different versions of the dipole model
with data recorded in ultraperipheral collisions at the LHC in order to
estimate the sensitivity of the data to gluon saturation in the target nuclei.
We find that ultraperipheral PbPb collisions indicate strong saturation effects
while $p$Pb collisions turn out to not have any discriminating power to
distinguish saturation from non-saturation scenarios.
