Generalising dexterous grasps to novel objects is an open problem. We show how to learn grasps for high DoF hands that generalise to novel objects, given as little as one demonstrated grasp. During grasp learning two types of probability density are learned that model the demonstrated grasp. The first density type (the contact model) models the relationship of an individual finger part to local surface features at its contact point. The second density type (the hand configuration model) models the whole hand configuration during the approach to grasp. When presented with a new object, many candidate grasps are generated, and a kinematically feasible grasp is selected that maximises the product of these densities. We demonstrate 31 successful grasps on novel objects (an 86% success rate), transferred from 16 training grasps. The method enables: transfer of dexterous grasps within object categories; across object categories; to and from objects where there is no complete model of the object available; and using two different dexterous hands.