  We prove that any Loewner PDE whose driving term h(z,t) vanishes at the
origin, and satisfies the bunching condition r m(Dh(0,t))\geq k(Dh(0,t)) for
some r\in R^+, admits a solution given by univalent mappings (f_t: B^q\to C^q).
This is done by discretizing time and considering the abstract basin of
attraction. If r<2, then the union of the images f_t(\B^q) of a such solution
is biholomorphic to C^q.
