  The effect of pasta phases on the quark-hadron phase transition is
investigated for a set of relativistic mean-field equations of state for both
hadron and quark matter. The results of the full numerical solution with pasta
phases are compared with those of an interpolating construction used in
previous works, for which we demonstrate an adequate description of the
numerical results. A one-to-one mapping of the free parameter of the
construction to the physical surface tension of the quark-hadron interface is
obtained for which a fit formula is given. For each pair of quark and hadron
matter models the critical value of the surface tension is determined, above
which the phase transition becomes close to the Maxwell construction. This
result agrees well with earlier theoretical estimates. The study is extended to
neutron star matter in beta equilibrium with electrons and muons and is applied
to investigate the effect of pasta phases on the structure of hybrid compact
stars and the robustness of a possible third family solution.
