  We first show that the intrinsic, geometrical structure of a dynamical
horizon is unique. A number of physically interesting constraints are then
established on the location of trapped and marginally trapped surfaces in the
vicinity of any dynamical horizon. These restrictions are used to prove several
uniqueness theorems for dynamical horizons. Ramifications of some of these
results to numerical simulations of black hole spacetimes are discussed.
Finally several expectations on the interplay between isometries and dynamical
horizons are shown to be borne out.
