  (abridged) We analyze the formation and migration of a proto-Jovian companion
in a circumstellar disk in 2d, during the period in which the companion makes
its transition from `Type I' to `Type II' migration, using a PPM code. Spiral
waves are generated by the gravitational torque of the planet on the disk.
Their effects are to cause the planet to migrate inward and the disk to form a
deep (low surface density) gap. Until a transition to slower Type II migration,
the migration rate of the planet is of order 1 AU/10$^3$ yr, and varies by less
than a factor of two with a factor twenty change in planet mass, but depends
near linearly on the disk mass. Although the disk is stable to self gravitating
perturbations (Toomre $Q>5$ everywhere), migration is faster by a factor of two
or more when self gravity is suppressed. Migration is equally sensitive to the
disk's mass distribution within 1--2 Hill radii of the planet, as demonstrated
by our simulations' sensitivity to the planet's assumed gravitational softening
parameter. Rapid migration can continue after gap formation. Gaps are typically
several AU in width and display the \mplan$^{2/3}$ proportionality predicted by
theory. Beginning from an initially unperturbed 0.05\msun disk, planets of mass
$M_{\rm pl}> 0.3$\mj can open a gap deep and wide enough to complete the
transition to slower \ttwo migration. Lower mass objects continue to migrate
rapidly, eventually impacting the inner boundary of our grid. This transition
mass is much larger than that predicted as the `Shiva mass' discussed in Ward
and Hahn (2000), making the survival of forming planets even more precarious
than they would predict.
