  We give a thorough investigation of sequences of uniformly rotating,
homogeneous axisymmetric Newtonian equilibrium configurations that bifurcate
from highly flattened Maclaurin spheroids. Each one of these sequences
possesses a mass-shedding limit. Starting at this point, the sequences proceed
towards the Maclaurin sequence and beyond. The first sequence leads to the well
known Dyson rings, whereas the end points of the higher sequences are
characterized by the formation of a two-body system, either a core-ring system
(for the second, the fourth etc. sequence) or a two-ring system (for the third,
the fifth etc. sequence). Although the general qualitative picture drawn by
Eriguchi and Hachisu in the eighties has been confirmed, slight differences
turned out in the interpretation of the origin of the first two-ring sequence
and in the general appearance of fluid bodies belonging to higher sequences.
