  We consider extremal limits of the recently constructed "subtracted
geometry". We show that extremality makes the horizon attractive against scalar
perturbations, but radial evolution of such perturbations changes the
asymptotics: from a conical-box to flat Minkowski. Thus these are black holes
that retain their near-horizon geometry under perturbations that drastically
change their asymptotics. We also show that this extremal subtracted solution
("subttractor") can arise as a boundary of the basin of attraction for flat
space attractors. We demonstrate this by using a fairly minimal action (that
has connections with STU model) where the equations of motion are integrable
and we are able to find analytic solutions that capture the flow from the
horizon to the asymptotic region. The subttractor is a boundary between two
qualitatively different flows. We expect that these results have
generalizations for other theories with charged dilatonic black holes.
