  We consider multimodal maps with holes and study the evolution of the open
systems with respect to equilibrium states for both geometric and H\"older
potentials. For small holes, we show that a large class of initial
distributions share the same escape rate and converge to a unique absolutely
continuous conditionally invariant measure; we also prove a variational
principle connecting the escape rate to the pressure on the survivor set, with
no conditions on the placement of the hole. Finally, introducing a weak
condition on the centre of the hole, we prove scaling limits for the escape
rate for holes centred at both periodic and nonperiodic points, as the diameter
of the hole goes to zero.
