  We present a detailed calculation of the distance-dependent two-point
function for quadrangulations with no multiple edges. Various discrete
observables measuring this two-point function are computed and analyzed in the
limit of large maps. For large distances and in the scaling regime, we recover
the same universal scaling function as for general quadrangulations. We then
explore the geometry of "minimal neck baby universes" (minbus), which are the
outgrowths to be removed from a general quadrangulation to transform it into a
quadrangulation with no multiple edges, the "mother universe". We give a number
of distance-dependent characterizations of minbus, such as the two-point
function inside a minbu or the law for the distance from a random point to the
mother universe.
