  We consider 5D braneworld models of quasi-localized gravity in which 4D
gravity is reproduced at intermediate scales while the extra dimension opens up
at both the very short and the very long distances, where the geometry is flat.
Our main interest is the interplay between the zero mode of these models,
whenever a normalizable zero mode exists, and the effects of zero energy
graviton resonant modes coming from the contributions of massive KK modes. We
first consider a compactified version of the GRS model and find that
quasi-localized gravity is characterized by a scale for which both the
resonance and the zero mode have significant contribution to 4D gravity. Above
this scale, gravity is primarily mediated by the zero mode, while the resonance
gives only minor corrections. Next, we consider an asymmetric version of the
standard non-compact GRS model, characterized by different cosmological
constants on each AdS side. We show that a resonance is present but the
asymmetry, through the form of the localizing potential, can weaken it,
resulting in a shorter lifetime and, thus, in a shorter distance scale for 4D
gravity. As a third model exhibiting quasi-localization, we consider a version
of the GRS model in which the central positive tension brane has been replaced
by a configuration of a scalar field propagating in the bulk.
