  We have compiled an extensive dataset on potential parts of the Monoceros
tidal stream and performed an exhaustive survey of dwarf galaxy semi-analytic
orbits in order to constrain its orbital properties. The best-fit orbits are
subsequently realized as self-consistent N-body simulations in order to
reproduce the spatial and velocity distribution of satellite debris. We find
that all kinematic and geometric constraints can be fit by a single stream
allowing for multiple wraps. The orbital eccentricity and inclination of the
progenitor are strongly constrained to be e = 0.10 \pm 0.05 and i = 25 \pm 5
deg. Ten new estimates of proper motions from the Sloan Digital Sky Survey
(SDSS) clearly exclude all retrograde orbits. Particles lost by the satellite
populate two, nearly concentric rings naturally explaining the detection of
stream stars at both 6--8 kpc (Ibata et al. 2003, Newberg et al. 2003) and
12--18 kpc (the Tri/And stream; Rocha-Pinto et al. 2003) from the Sun. We have
attempted to predict the present location of the Monoceros stream progenitor
using different information: (i) the kinematical and spatial distribution of
detections and (ii) the different mean metallicity in the innner and the outer
rings. A current location at l ~ 245, b ~ -18., with a distance to the Sun
r_s~15 kpc, reproduces the available constraints. The mass of the progenitor
has been poorly determined due to the slow orbital decay. Similar fits have
been obtained for masses (3-9)10^8 M_sun. Additionally, we have analyzed to
possible common origin of the Canis Major dwarf and the Monoceros stream,
unfortunately, without a conclusive result.
