The explosive growth and diversity of machine learning applications motivate a fundamental rethinking of learning with mobile and edge devices. How can we address diverse/disparate client goals and learn with scarce heterogeneous data? While federated learning aims to address these issues, it has several bottlenecks and challenges hindering a unified solution. On the other hand, large transformer models have been shown to work across a variety of tasks often achieving remarkable few-shot adaptation. This raises the question: Can clients use a single generalpurpose model -rather than custom models for each task -while obeying device and network constraints? In this work, we investigate pretrained transformers (PTF) to achieve these on-device learning goals and thoroughly explore the roles of model size and modularity, where the latter refers to adaptation through modules such as prompts or adapters. Focusing on federated learning, we demonstrate that:(1) Larger scale shrinks the accuracy gaps between alternative approaches and improves heterogeneity robustness. Scale allows clients to run more local SGD epochs which can significantly reduce the number of communication rounds. At the extreme, clients can achieve respectable accuracy fully-locally highlighting the potential of fully-local learning. (2) Modularity, by design, enables >100× less communication in bits. Surprisingly, it also boosts the generalization capability of local adaptation methods and the robustness of smaller PTFs. Finally, it enables clients to solve multiple unrelated tasks simultaneously using a single PTF, whereas full updates are prone to catastrophic forgetting. These insights on scale and modularity motivate a new federated learning approach we call "You Only Load Once" (FedYolo): The clients load a full PTF model once and all future updates are accomplished through communication-efficient modules with limited catastrophic-forgetting, where each task is assigned to its own module.