Multilingual pretrained language models have demonstrated remarkable zero-shot cross-lingual transfer capabilities. Such transfer emerges by fine-tuning on a task of interest in one language and evaluating on a distinct language, not seen during the fine-tuning. Despite promising results, we still lack a proper understanding of the source of this transfer. Using a novel layer ablation technique and analyses of the model's internal representations, we show that multilingual BERT, a popular multilingual language model, can be viewed as the stacking of two sub-networks: a multilingual encoder followed by a task-specific language-agnostic predictor. While the encoder is crucial for cross-lingual transfer and remains mostly unchanged during fine-tuning, the task predictor has little importance on the transfer and can be reinitialized during fine-tuning. We present extensive experiments with three distinct tasks, seventeen typologically diverse languages and multiple domains to support our hypothesis.