  Two-dimensional semiconductor quantum dots are studied in the the
filling-factor range 2<v<3. We find both theoretical and experimental evidence
of a collective many-body phenomenon, where a fraction of the trapped electrons
form an incompressible spin-droplet on the highest occupied Landau level. The
phenomenon occurs only when the number of electrons in the quantum dot is
larger than ~30. We find the onset of the spin-droplet regime at v=5/2. This
proposes a finite-geometry alternative to the Moore-Read-type Pfaffian state of
the bulk two-dimensional electron gas. Hence, the spin-droplet formation may be
related to the observed fragility of the v=5/2 quantum Hall state in narrow
quantum point contacts.
