TeV-scale gravity theories allow the possibility of producing small black holes at energies that soon will be explored at the LHC or at the Auger observatory. One of the expected signatures is the detection of Hawking radiation, that might eventually terminate if the black hole, once perturbed, leaves the brane. Here, we study how the `black hole plus brane' system evolves once the black hole is given an initial velocity, that mimics, for instance, the recoil due to the emission of a graviton. The results of our dynamical analysis show that the brane bends around the black hole, suggesting that the black hole eventually escapes into the extra dimensions once two portions of the brane come in contact and reconnect. This gives a dynamical mechanism for the creation of baby branes.