  The lowest-Landau-level anyon model becomes nonperiodic in the statistics
parameter when the finite size of the attached flux tubes is taken into
account. The finite-size effects cause the inverse proportional relation
between the critical filling factor and the statistics parameter to be
nonperiodically continued in the screening regime, where the fluxes are
anti-parallel to the external magnetic field -- at critical filling, the
external magnetic field is entirely screened by the mean magnetic field
associated with the flux tubes. A clustering argument is proposed to select
particular values of the statistics parameter. In this way, IQHE and FQHE
fillings are obtained in terms of gapped nondegenerate LLL-anyonic wave
functions. Jain's series are reproduced without the need to populate higher
Landau levels. New FQHE series are proposed, like, in particular, the
particle-hole complementary series of the Laughlin one. For fast-rotating
Bose-Einstein condensates, a corresponding clustering argument yields
particular fractional filling series.
