We consider the ''fractional quantum Hall atom'' in the vanishing Zeem
an energy limit, and investigate the validity of Hund's maximum-spin r
ule for interacting electrons in various Landau levels. While it is no
t valid for electrons in the lowest Landau level, it generally predict
s the ground-state spin correctly provided it is applied to composite
fermions. The composite fermion theory also reveals a ''self-similar''
structure in the filling factor range 4/3 > upsilon > 2/3.