This paper serves to introduce the Align, Minimize and Diversify (AMD) method, a Source-Free Unsupervised Domain Adaptation approach for Handwritten Text Recognition (HTR). This framework decouples the adaptation process from the source data, thus not only sidestepping the resource-intensive retraining process but also making it possible to leverage the wealth of pre-trained knowledge encoded in modern Deep Learning architectures. Our method explicitly eliminates the need to revisit the source data during adaptation by incorporating three distinct regularization terms: the Align term, which reduces the feature distribution discrepancy between source and target data, ensuring the transferability of the pre-trained representation; the Minimize term, which encourages the model to make assertive predictions, pushing the outputs towards one-hot-like distributions in order to minimize prediction uncertainty, and finally, the Diversify term, which safeguards against the degeneracy in predictions by promoting varied and distinctive sequences throughout the target data, preventing informational collapse. Experimental results from several benchmarks demonstrated the effectiveness and robustness of AMD, showing it to be competitive and often outperforming DA methods in HTR.