  We analyze a real one-parameter family of quasiconformal deformations of a
hyperbolic rational map known as {\em spinning}. We show that under fairly
general hypotheses, the limit of spinning either exists and is unique, or else
converges to infinity in the moduli space of rational maps of a fixed degree.
When the limit exists, it has either a parabolic fixed point, or a pre-periodic
critical point in the Julia set, depending on the combinatorics of the data
defining the deformation. The proofs are soft and rely on two ingredients: the
construction of a Riemann surface containing the closure of the family, and an
analysis of the geometric limits of some simple dynamical systems.
  An interpretation in terms of Teichm\"uller theory is presented as well.
