  Gas giant planets are expected to accrete most of their mass via a
circumplanetary disk. If the planet is unmagnetized and initially slowly
rotating, it will accrete gas via a radially narrow boundary layer and rapidly
spin up. Radial broadening of the boundary layer as the planet spins up reduces
the specific angular momentum of accreted gas, allowing the planet to find a
terminal rotation rate short of the breakup rate. Here, we use axisymmetric
viscous hydrodynamic simulations to quantify the terminal rotation rate of
planets accreting from their circumplanetary disks. For an isothermal
planet-disk system with a disk scale height $h/r =0.1$ near the planetary
surface, spin up switches to spin down at between 70\% and 80\% of the planet's
breakup angular velocity. In a qualitative difference from vertically-averaged
models -- where spin down can co-exist with mass accretion -- we observe
\emph{decretion} accompanying solutions where angular momentum is being lost.
The critical spin rate depends upon the disk thickness near the planet. For an
isothermal system with a disk scale height of $h/r = 0.15$ near the planet, the
critical spin rate drops to between 60\% and 70\% of the planet's breakup
angular velocity. In the disk outside the boundary layer, we identify
meridional circulation flows, which are unsteady and instantaneously asymmetric
across the mid-plane. The simulated flows are strong enough to vertically
redistribute solid material in early-stage satellite formation. We discuss how
extrasolar planetary rotation measurements, when combined with spectroscopic
and variability studies of protoplanets with circumplanetary disks, could
determine the role of magnetic and non-magnetic processes in setting giant
planet spins.
