Super-Brownian motions in higher dimensions with absolutely continuous measure states.

Continuous super-Brownian motions in two and higher dimensions are known to have singular measure states. However, by weakening the branching mechanism in an irregular way they can be forced to have absolutely continuous states. The sufficient conditions we impose are identified in a couple of examples with irregularities in only one coordinate. This includes the case of branching restricted to some densely situated ensemble of hyperplanes