  Gas giant planets are believed to accrete from their circumplanetary disks
(CPDs). The CPDs usually involve accretion through the boundary layer (BL) in
the vicinity of planets. Prior studies have concentrated on the BL of
non-spinning planets. We investigate the influence of planetary spin on the
wave behaviors within the BL. The rotation profile in such BLs would show sharp
transition from the rigid rotation to the Keplerian rotation. We examine the
angular momentum transport in these BL in terms of linear perturbation
analysis. We find that the global inertia-acoustic mode associated with
spinning planets would give rise to the inflow of angular momentum and the
accretion of gas. In this work, we identify a new kind of global mode, namely
the Rossby mode. The Rossby mode can lead to the outflow of angular momentum
and the decretion of gas from a spinning planet. The Rossby mode provide a
negative feedback that regulates the planetary spin and mass. We compare the
growth rate of the two modes as a function of the width of BL, the Mach number
and the spin rate of planet. Our results reveal the underlying hydrodynamic
mechanism of terminal spins and asymptotic mass of the giant planets.
