For a generic single-input planar control system (x)over dot = F(x) +uG(x), x is an element of R-2, u is an element of [-1,1], F( 0) = 0, we analyze the properties of abnormal extremals for the minimum time stabilization to the origin. We prove that abnormal extremals are finite concatenations of bang arcs with switchings occurring on the set in which the vector fields F and G are collinear. Moreover, all the generic singularities of one parametric family of extremal trajectories near to abnormal extremals are studied. In particular, we prove that all possible sequences of these singularities, and hence all generic abnormal extremals, can be classified by a set of words recognizable by an automaton.