  We use the modified quark-meson coupling (MQMC) model to study the
composition profile of neutron star matter and compare the results with those
calculated by quantum hadrodynamics (QHD). Both MQMC and QHD model parameters
are adjusted to produce exactly the same saturation properties so that we can
investigate the model dependences of the matter composition at high densities.
We consider the possibility of deep kaon optical potential and find that the
composition of matter is very sensitive to the interaction strength of kaons
with matter. The onset densities of the kaon condensation are studied in detail
by varying the kaon optical potentials. We find that the MQMC model produces
the kaon condensation at lower densities than QHD. The presence of kaon
condensation changes drastically the population of octet baryons and leptons.
Once the kaon condensation takes place, the population of kaons builds up very
quickly, and kaons become the dominant component of the matter. We find that
the $\omega$-meson plays an important role in increasing the kaon population
and suppressing the hyperon population.
