  In this note the result by A. Swift concerning the embeddability of countably
branching bundle graphs into Banach spaces is extended from the context of
reflexive spaces with an unconditional asymptotic structure to the context of
dual spaces with a weak$^*$ unconditional asymptotic structure. We also
investigate weak$^*$ asymptotic midpoint uniform convexity in dual spaces which
turns out to be equivalent to its weak version in general and to the standard
weak$^*$ asymptotic uniform convexity up to renorming in dual spaces with a
weak$^*$ unconditional asymptotic structure.
