  In Part II of this study we consider two cases of three-phase coexistence.
First, the capped capillary may allow for vapour, drop-like, and slab-like
phases to coexist at the same values of temperature and chemical potential.
Second, the slit pore forming the bulk of the capped capillary may allow for
the coexistence between vapour, planar prewetting film and capillary-liquid.
While the consideration of the former case allows us to summarise the
phenomenology presented in Part I and to show that the transition line of wedge
prewetting is shifted in capillary-like geometries by a constant value,
depending on the capillary width, the careful examination of the latter case
allows us to uncover a new phase transition in confined fluids, a continuous
planar prewetting transition. A planar prewetting transition is known to be a
distinctly first-order phenomenon, and typically taking place on the scale of
several atomic diameters. A continuous prewetting transition, on the other
hand, is scale invariant. Thus, apart from being of fundamental significance,
this finding has potential for facilitating experimental detection as well as
measurements of planar prewetting. Further, we provide proof for the existence
of a tri-critical point of the three-phase coexistence line of the capped
capillary while by considering a dynamic model of wetting we show how the
relaxation of the system can be pinned by a metastable state. We present a full
parametric study of our model system and support our findings with exhaustive
examples of density profiles, adsorption and free energy isotherms, and full
phase diagrams.
