A nonparametric model is introduced that allows multiple related regression tasks to take inputs from a common data space. Traditional transfer learning models can be inappropriate if the dependence among the outputs cannot be fully resolved by known input-specific and task-specific predictors. The proposed model treats such output responses as conditionally independent, given known predictors and appropriate unobserved random effects. The model is nonparametric in the sense that the dimensionality of random effects is not specified a priori but is instead determined from data. An approach to estimating the model is presented uses an EM algorithm that is efficient on a very large scale collaborative prediction problem. The obtained prediction accuracy is competitive with state-of-the-art results.