  We present the first characterisation of the 12um warm dust ("exo-Zodi")
luminosity function around Sun-like stars, focussing on the dustiest systems
that can be identified by WISE. We detect six new warm dust candidates, five of
which have unknown ages. We show that the dustiest old (>Gyr) systems like
BD+20 307 are 1 in 10,000 occurrences. Bright warm dust is more common around
young (<120Myr) systems, with a ~1% occurrence rate. We show that a two
component in situ model where all stars have initially massive warm disks and
in which warm debris is also generated at some random time along the stars'
main-sequence lifetime, perhaps due to a collision, can explain the
observations. However, if all stars only have initially massive warm disks
these would not be visible at Gyr ages, and random collisions on the
main-sequence are too infrequent to explain the high disk occurrence rate for
young stars. That is, neither component can explain the observations on their
own. Despite these conclusions, we cannot rule out an alternative model in
which comets are scattered from outer regions because the distribution of
systems with the appropriate dynamics is unknown. Our in situ model predicts
the fraction of stars with exo-Zodi bright enough to cause problems for future
exo-Earth imaging attempts is at least ~10%, and is higher for populations of
stars younger than a few Gyr. This prediction of ~10% applies to old stars
because bright systems like BD+20 307 imply a population of fainter systems
that were once bright but are now decaying through fainter levels. Our
prediction should be strongly tested by the Large Binocular Telescope
Interferometer, providing valuable input for more detailed evolution models. A
detection fraction lower than our prediction could indicate that the hot dust
in systems like BD+20 307 has a cometary origin due to the quirks of the
planetary dynamics.
