The pickup of alkali atoms by helium nanodroplets is unusual in that these atoms are not wetted and enveloped by the liquid, but reside in weakly binding surface dimples. As a result, it has been suggested that the alkali clusters which assemble on droplet surfaces must exist in spin-polarized states with a low condensation energy. We consider the size distribution statistics which would be exhibited by the alkali agglomerates in such a case, and show that it would be very different from the conventional Poisson shape. A careful measurement of the variation of the intensities of droplet-grown alkali clusters with size and/or vapor pressure in the pickup region may be able to test the giant-spin hypothesis. (C) 2003 American Institute of Physics.