  We assemble 121 spectroscopically-confirmed halo carbon stars, drawn from the
literature, exhibiting measurable variability in the Catalina Surveys. We
present their periods and amplitudes, which are used to estimate distances from
period-luminosity relationships. The location of the carbon stars - and their
velocities when available - allow us to trace the streams of the Sagittarius
(Sgr) dwarf spheroidal galaxy. These are compared to a canonical numerical
simulation of the accretion of Sgr. We find that the data match this model well
for heliocentric distances of 15-50 kpc, except for a virtual lack of carbon
stars in the trailing arm just north of the Galactic Plane, and there is only
tentative evidence of the leading arm south of the Plane. The majority of the
sample can be attributed to the Sgr accretion. We also find groups of carbon
stars which are not part of Sgr; most of which are associated with known halo
substructures. A few have no obvious attribution and may indicate new
substructure. We find evidence that there may be a structure behind the Sgr
leading stream apocentre, at ~100 kpc, and a more distant extension to the
Pisces Overdensity also at ~100 kpc. We study a further 75 carbon stars for
which no good period data could be obtained, and for which NIR magnitudes and
colours are used to estimate distances. These data add support for the features
found at distances beyond 100 kpc.
