  A one dimensional sublimation model for cometary nuclei is used to derive
size limits for the nuclei of sungrazing comets, and to estimate oxygen ion
fluxes at 1 AU from their evaporation. Given that none of the ~300 sungrazers
detected by the SOlar and Heliospheric Observatory (SOHO) was observed after
disappearing behind the sun, and that small nuclei with a radius of ~3.5m could
be observed, it is assumed that all SOHO sungrazers were completely destroyed.
For the case that sublimation alone is sufficient for destruction, the model
yields an upper size limit as a function of nuclear density, albedo and
perihelion distance. If the density of the nuclei is that typical of porous ice
(600kg/m^3), the maximum size is 63m. These results confirm similar model
calculations by Weissman (1983). An analytical expression is derived that
approximates the model results well. We discuss possible modifications of our
results by different disruption mechanisms. While disruption by thermal stress
does not change the upper size limits significantly, they may be somewhat
increased by tidal disruption (up to 100m for a density of 600kg/m^3) dependent
on the isotropy of the sublimation process and the tensile strength of the
comet. Implications for the Kreutz family of sungrazers are discussed.
  Oxygen ions from the sublimation of sungrazing comets form a tail. Fluxes
from this tail are sufficiently high to be measured at 1 AU by particle
detectors on spacecraft, but the duration of a tail crossing is only about half
an hour. Therefore the probability of a spacecraft actually encountering a tail
of an evaporating sungrazer is only of the order of two percent per year.
