Trapped surfaces are the precursors of singularities in
gravitational collapse. In numerical simulations it has been found that trapped surfaces sometimes make sudden "jumps" from one location to another. When a lump of matter hits a trapped surface it is believed
that the trapped surface moves outwards. This behaviour is difficult to describe analytically in a 3+1-dimensional spacetime because gravitational radiation is emitted. The problem is more easily tackled in 2+1 dimensions. By considering a toy model of a black hole in 2+1-dimensional anti-de Sitter space, and letting a point particle fall into the black hole, an exact description of this peculiar behaviour of the trapped surfaces can be found.