The (m-vector) k-constrained Kadomtsev-Petviashvili (KP) hierarchy is shown
to be a "pseudo"-reduction of the (m+1)-component KP hierarchy. To facilit
ate the implementation of this reduction on the level of the solutions, the
typical multi-component KP solutions are mapped onto solutions of a Toda m
olecule-type equation from which (Wronskian and Grammian) solutions for the
constrained KP hierarchy follow. The reduction of the associated linear sy
stems is discussed and its importance for the choice of bilinear representa
tion of the reduced systems is explained. (C) 1999 American Institute of Ph
ysics. [S0022-2488(99)01310-9].