As of today, object categorization algorithms are not able to achieve the level of robustness and generality necessary to work reliably in the real world. Even the most powerful convolutional neural network we can train fails to perform satisfactorily when trained and tested on data from different databases. This issue, known as domain adaptation and/or dataset bias in the literature, is due to a distribution mismatch between data collections. Methods addressing it go from max-margin classifiers to learning how to modify the features and obtain a more robust representation. Recent work showed that by casting the problem into the image-to-class recognition framework, the domain adaptation problem is significantly alleviated \cite{danbnn}. Here we follow this approach, and show how a very simple, learning free Naive Bayes Nearest Neighbor (NBNN)-based domain adaptation algorithm can significantly alleviate the distribution mismatch among source and target data, especially when the number of classes and the number of sources grow. Experiments on standard benchmarks used in the literature show that our approach (a) is competitive with the current state of the art on small scale problems, and (b) achieves the current state of the art as the number of classes and sources grows, with minimal computational requirements.