  Recent observational data suggests a high compacticity (the quotient M/R) of
some "neutron" stars. Motivated by these works we revisit models based on
quark-diquark degrees of freedom and address the question of whether that
matter is stable against diquark disassembling and hadronization within the
different models. We find that equations of state modeled as effective $\lambda
\phi^{4}$ theories do not generally produce stable self-bound matter and are
not suitable for constructing very compact star models, that is the matter
would decay into neutron matter. We also discuss some insights obtained by
including hard sphere terms in the equation of state to model repulsive
interactions. We finally compare the resulting equations of state with previous
models and emphasize the role of the boundary conditions at the surface of
compact self-bound stars, features of a possible normal crust of the latter and
related topics.

Astrophysics