  We consider the phantom braneworld model in the context of the maximum turn
around radius, $R_{\rm TA,max}$, of a stable, spherical cosmic structure with a
given mass. The maximum turn around radius is the point where the attraction
due to the central inhomogeneity gets balanced with the repulsion of the
ambient dark energy, beyond which a structure cannot hold any mass, thereby
giving the maximum upper bound on the size of a stable structure. In this work
we derive an analytical expression of $R_{\rm TA,max}$ for this model using
cosmological scalar perturbation theory. Using this we numerically constrain
the parameter space, including a bulk cosmological constant and the Weyl fluid,
from the mass versus observed size data for some nearby, non-virial cosmic
structures. We use different values of the matter density parameter $\Omega_m$,
both larger and smaller than that of the $\Lambda{\rm CDM}$, as the input in
our analysis. We show in particular, that a) with a vanishing bulk cosmological
constant the predicted upper bound is always greater than what is actually
observed; similar conclusion holds if the bulk cosmological constant is
negative b) if it is positive, the predicted maximum size can go considerably
below than what is actually observed and owing to the involved nature of the
field equations, it leads to interesting constraints on not only the bulk
cosmological constant itself but on the whole parameter space of the theory.
