The search for the existence of pasta phases
in the low density regions of nuclear and neutron star matter is performed within the context of the quark-meson
coupling (QMC) model, which incorporates quark
degrees of freedom.
Fixed proton fractions are considered, as well as nuclear matter in
beta equilibrium at zero temperature. We discuss the recent
attempts to better understand the surface energy in the coexistence
phases regime and we present results that show the existence of the
pasta phases subject to some choices of the surface energy coefficient.
We also analyse the influence of the nuclear pasta on some neutron