  (abridged) We construct quark-diquark equations of state using the quark mass
density-dependent formalism. A region inside a $2-D$ parameter space in which
this matter is absolutely stable is identified. Motivated by the reported
compactness of some neutron star candidates we present stellar sequences and
show that the quark-diquark EOSs allow a very compact structure, even in the
cases in which the diquark itself is not bound.
