Revisiting black holes of algebraic type D with a cosmological constant

As an extension of our previous work [H. Ovcharenko et al. Phys. Rev. D 111, 024038 (2025)], we study a complete family of type D black holes with Kerr-like rotation, Newman-Unti-Tamburino (NUT) twist, acceleration, electric and magnetic charges, and any value of the cosmological constant $\mathrm{\ensuremath{\Lambda}}$. We relate various metric forms of these spacetimes, namely those found by Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski-Demia\ifmmode \acute{n}\else \'{n}\fi{}ski, Griffiths-Podolsk\'y, and most recently Astorino. By explicit coordinate transformations and proper identification of the physical parameters we show that these representations are locally equivalent, and cover the entire class of type D solutions of the Einstein-Maxwell-$\mathrm{\ensuremath{\Lambda}}$ equations, such that the (non-null) electromagnetic field is aligned with both the (double-degenerate) principal null directions of the Weyl tensor. In particular, we concentrate on the subclass which describes accelerating NUT black holes without the Kerr-like rotation.