  We use the covariant spectator theory with an effective quark-antiquark
interaction, containing Lorentz scalar, pseudoscalar, and vector contributions,
to calculate the masses and vertex functions of, simultaneously, heavy and
heavy-light mesons. We perform least-square fits of the model parameters,
including the quark masses, to the meson spectrum and systematically study the
sensitivity of the parameters with respect to different sets of fitted data. We
investigate the influence of the vector confining interaction by using a
continuous parameter controlling its weight. We find that vector contributions
to the confining interaction between 0% and about 30% lead to essentially the
same agreement with the data. Similarly, the light quark masses are not very
tightly constrained. In all cases, the meson mass spectra calculated with our
fitted models agree very well with the experimental data. We also calculate the
mesons wave functions in a partial wave representation and show how they are
related to the meson vertex functions in covariant form.
