  A homogeneous Gibbons-Hawking ansatz is described, leading to 4-dimensional
hyperkahler metrics with homotheties. In combination with Blaschke products on
the unit disc in the complex plane, this ansatz allows one to construct
infinite-dimensional families of such hyperkahler metrics that are, in a
suitable sense, complete. Our construction also gives rise to incomplete
metrics on 3-dimensional contact manifolds that induce complete
Carnot-Caratheodory distances.
