Abstract: We study design of black-box model extraction attacks that can *send minimal number of queries from* a *publicly available dataset* to a target ML model through a predictive API with an aim *to create an informative and distributionally equivalent replica* of the target.First, we define *distributionally equivalent* and *Max-Information model extraction* attacks, and reduce them into a variational optimisation problem. The attacker sequentially solves this optimisation problem to select the most informative queries that simultaneously maximise the entropy and reduce the mismatch between the target and the stolen models. This leads to *an active sampling-based query selection algorithm*, Marich, which is *model-oblivious*. Then, we evaluate Marich on different text and image data sets, and different models, including CNNs and BERT. Marich extracts models that achieve $\sim 60-95\%$ of true model's accuracy and uses $\sim 1,000 - 8,500$ queries from the publicly available datasets, which are different from the private training datasets. Models extracted by Marich yield prediction distributions, which are $\sim2-4\times$ closer to the target's distribution in comparison to the existing active sampling-based attacks. The extracted models also lead to 84-96$\%$ accuracy under membership inference attacks. Experimental results validate that Marich is *query-efficient*, and capable of performing task-accurate, high-fidelity, and informative model extraction.