The familiar picture of magnetic collimation of jets is critiqued. Sol
utions are derived that explicitly demonstrate the asymptotically para
bolic nature of almost all stream lines, more or less consistent with
previous discussions. It is then shown that collimation is too slow to
be physically relevant when the flow in its uncollimated state is onl
y weakly magnetized. In the alternative and more popular case, where t
he magnetic field is dynamically significant at all points on the flow
, the divergence of field lines to large cylindrical radius implies ki
nk instability. It is shown that the kink instability, for astrophysic
al parameters, is not expected to stabilize at finite amplitudes, and
that magnetically confined jets should therefore be limited to modest
collimation in the absence of an additional collimation mechanism. It
is conjectured that the kink instability can be mitigated if the jet h
as inner and outer parts, with only the latter strongly magnetized, as
previously proposed by Shu and coworkers for other reasons. The possi
bility is also considered that magnetic collimation is intrinsically m
odest.