Humans are remarkably adept at generalizing knowledge between experiences in a way that can be difficult for computers. Often, this entails generalizing constituent pieces of experiences that do not fully overlap, but nonetheless share useful similarities with, previously acquired knowledge. However, it is often unclear how knowledge gained in one context should generalize to another. Previous computational models and data suggest that rather than learning about each individual context, humans build latent abstract structures and learn to link these structures to arbitrary contexts, facilitating generalization. In these models, task structures that are more popular across contexts are more likely to be revisited in new contexts. However, these models can only re-use policies as a whole and are unable to transfer knowledge about the transition structure of the environment even if only the goal has changed (or vice-versa). This contrasts with ecological settings, where some aspects of task structure, such as the transition function, will be shared between context separately from other aspects, such as the reward function. Here, we develop a novel non-parametric Bayesian agent that forms independent latent clusters for transition and reward functions, affording separable transfer of their constituent parts across contexts. We show that the relative performance of this agent compared to an agent that jointly clusters reward and transition functions depends environmental task statistics: the mutual information between transition and reward functions and the stochasticity of the observations. We formalize our analysis through an information theoretic account of the priors, and propose a meta learning agent that dynamically arbitrates between strategies across task domains to optimize a statistical tradeoff.