  We show that a totally dissipative system has all nonsingular systems as
factors, but that this is no longer true when the factor maps are required to
be finitary. In particular, if a nonsingular Bernoulli shift satisfies the
Doeblin condition, and has a limiting marginal distribution p, then it cannot
have, as a finitary factor, an independent and identically distributed (iid)
system of entropy larger than H(p); on the other hand, we show that iid systems
with entropy strictly lower than H(p) can be obtained as finitary factors of
these Bernoulli shifts, extending Keane and Smorodinsky's finitary version of
Sinai's factor theorem to the nonsingular setting. As a consequence of our
results we also obtain that every transitive twice continuously differentiable
Anosov diffeomorphism on a compact manifold, endowed with volume measure, has
iid factors, and if the factor is required to be finitary, then the iid factor
cannot have Kolmogorov-Sinai entropy greater than the measure-theoretic entropy
of a Sinai-Ruelle-Bowen measure associated with the Anosov diffeomorphism.
