  Most studies concerning the growth and evolution of massive planets focus
either on their accretion or their migration only. In this work we study both
processes concurrently to investigate how they might mutually affect each
other. We modeled a 2-dimensional disk with a steady accretion flow onto the
central star and embed a Jupiter mass planet at 5.2 au. The disk is locally
isothermal and viscosity is modeled using a constant $\alpha$. The planet is
held on a fixed orbit for a few hundred orbits to allow the disk to adapt and
carve a gap. After this period, the planet is released and free to move
according to the gravitational interaction with the gas disk. The mass
accretion onto the planet is modeled by removing a fraction of gas from the
inner Hill sphere, and the removed mass and momentum can be added to the
planet. Our results show that a fast migrating planet is able to accrete more
gas than a slower migrating planet. Utilizing a tracer fluid we analyzed the
origin of the accreted gas which comes predominantly originating from the inner
disk for a fast migrating planet. In case of slower migration the fraction of
gas from the outer disk increases. We also found that even for very high
accretion rates in some cases gas crosses the planetary gap from the inner to
the outer disk. Our simulations show that the crossing of gas changes during
the migration process as the migration rate slows down. Therefore classical
type II migration where the planet migrates with the viscous drift rate and no
gas crosses the gap is no general process but may only occur for special
parameters and at a certain time during the orbital evolution of the planet.
