  Null and timelike geodesics around a 2+1 black hole are determined. Complete
geodesics of both types exist in the rotating black-hole background, but not in
the spinless case. Upper and lower bounds for the radial size of the orbits are
given in all cases and the possibility of passing from one black hole exterior
spacetime to another is discussed using the Penrose diagrams. An analysis of
particle motions by means of effective potentials and orbit graphs are also
included.
