  We look for solutions in Einstein gravity corresponding to inflating
braneworlds of arbitrary dimension and co-dimension. These solutions correspond
to isolated sources (no long range fields). Using dynamical systems techniques,
we show that there exists a unique solution corresponding to a black $p$-brane
with a regular horizon at the location of the brane. The solution is {\it not}
however asymptotically flat, but has global deficit angles.
