  All asteroids are currently classified as either family, originating from the
disruption of known bodies, or non-family. An outstanding question is the
origin of these non-family asteroids. Were they formed individually, or as
members of known families but with chaotically evolving orbits, or are they
members of old ghost families, that is, asteroids with a common parent body but
with orbits that no longer cluster in orbital element space? Here, we show that
the sizes of the non-family asteroids in the inner belt are correlated with
their orbital eccentricities and anticorrelated with their inclinations,
suggesting that both non-family and family asteroids originate from a small
number of large primordial planetesimals. We estimate that ~85% of the
asteroids in the inner main belt originate from the Flora, Vesta, Nysa, Polana
and Eulalia families, with the remaining ~15% originating from either the same
families or, more likely, a few ghost families. These new results imply that we
must seek explanations for the differing characteristics of the various
meteorite groups in the evolutionary histories of a few, large, precursor
bodies. Our findings also support the model that asteroids formed big through
the gravitational collapse of material in a protoplanetary disk.
