  We study spin fragmentation of an antiferromagnetic spin 1 condensate in the
presence of a quadratic Zeeman (QZ) effect breaking spin rotational symmetry.
We describe how the QZ effect turns a fragmented spin state, with large
fluctuations of the Zeemans populations, into a regular polar condensate, where
atoms all condense in the $m=0$ state along the field direction. We calculate
the average value and variance of the Zeeman state $m=0$ to illustrate clearly
the crossover from a fragmented to an unfragmented state. The typical width of
this crossover is $q \sim k_B T/N$, where $q$ is the QZ energy, $T$ the spin
temperature and $N$ the atom number. This shows that spin fluctuations are a
mesoscopic effect that will not survive in the thermodynamic limit
$N\rightarrow \infty$, but are observable for sufficiently small atom number.
