Asymptotically flat black holes in 2 + 1 dimensions are a rarity. We study the recently found black flower solutions (asymptotically flat black holes with deformed horizons), static black holes, rotating black holes and the dynamical black flowers (black holes with radiative gravitons) of the purely quadratic version of new massive gravity. We show how they appear in this theory and we also show that they are also solutions to the infinite order extended version of the new massive gravity, that is the Born-Infeld extension of new massive gravity with an amputated Einsteinian piece. The same metrics also solve the topologically extended versions of these theories, with modified conserved charges and the thermodynamical quantities, such as the Wald entropy. Besides these we find new conformally flat radiating type solutions to these extended gravity models. We also show that these metrics do not arise in Einstein's gravity coupled to physical perfect fluids.