MHD winds can emanate from both stars and surrounding disks. When the two s
ystems are coupled by accretion, it is of interest to know how much wind po
wer is available and which (if either) of the two rotators dominates that p
ower. We investigate this in the context of multipolar planetary nebulae (P
Ns) and protoplanetary nebulae (PPNs), for which recent observations have r
evealed the need for a wind power source in excess of that available from r
adiation driving and a possible need for magnetic shaping. We calculate the
MHD wind power from a coupled disk and star, where the former results from
binary disruption. The resulting wind powers depend only on the accretion
rate and stellar properties. We find that if the stellar envelope were init
ially slowly rotating, the disk wind would dominate throughout the evolutio
n. If the envelope of the star were rapidly rotating, the stellar wind coul
d initially be of comparable power to the disk wind until the stellar wind
carries away the star's angular momentum. Since an initially rapidly rotati
ng star can have its spin and magnetic axes misaligned to the disk, multipo
lar out-flows can result from this disk wind system. For times greater than
a spin-down time, the post-asymptotic giant branch stellar wind is slaved
to the disk for both slow and rapid initial spin cases, and the disk wind l
uminosity dominates. We find a reasonably large parameter space where a hyb
rid star+disk MHD-driven wind is plausible and where both or either can acc
ount for PPN and PN powers. We also speculate on the morphologies which may
emerge from the coupled system. The coupled winds might help explain the s
hapes of a number of remarkable multishell or multipolar nebulae. Magnetic
activity such as X-ray flares may be associated with both the central star
and the disk and would be a valuable diagnostic for the dynamical role of M
HD processes in PNs.