  We study finite dimensional almost and quasi-effective prolongations of
nilpotent Z-graded Lie algebras, especially focusing on those having a
decomposable reductive structural subalgebra. Our assumptions generalize
effectiveness and algebraicity and are appropriate to obtain Levi-Mal\v{c}ev
and Levi-Chevalley decompositions and precisions on the heigth and other
properties of the prolongations in a very natural way. In a last section we
systematically present examples in which simple Lie algebras are obtained as
prolongations, for reductive structural algebras of type A, B, C and D, of
nilpotent Z-graded Lie algebras arising as their linear representations.
