Are Superentropic black holes superentropic?

We study a critical limit in which asymptotically-AdS black holes develop maximal conical deficits and their horizons become non-compact. When applied to stationary rotating black holes this limit coincides with the "ultraspinning limit" and yields the Superentropic black holes whose entropy was derived recently and found to exceed the maximal possible bound imposed by the Reverse Isoperimetric Inequality. To gain more insight into this peculiar result, we study this limit in the context of accelerated AdS black holes that have unequal deficits along the polar axes, hence the maximal deficit need not appear on both poles simultaneously. Surprisingly, we find that in the presence of acceleration, the critical limit becomes smooth, and is obtained simply by taking various upper bounds in the parameter space that we elucidate. The Critical black holes thus obtained have many common features with Superentropic black holes, but are manifestly not superentropic. This raises a concern as to whether Superentropic black holes actually are superentropic. We argue that this may not be so and that the original conclusion is likely attributed to the degeneracy of the resulting first law.