  The slow rotation of some young stars and the extreme rotation periods of
some Ap stars have so far defied explanation. The absence of sufficiently
efficient braking mechanisms for newly formed stars points to the star
formation process itself as the origin. I find that a mode of star formation
exists by which a protostar can form without accreting angular momentum. It
depends on the survival of a magnetic connection between the accreting matter
and the birth cloud. The conditions for this process to operate are analyzed,
and illustrated with a generic (scale-free) model. Depending on the initial
rotation rate of the accreting matter, either a Keplerian disk forms, or the
gas ends up rotating with the rotation period of the cloud, even if it is at a
large distance. The boundary in parameter space between these two outcomes is
sharp.
