  In a attempt to treat a supergravity as a tensor representation, the
4-dimensional N-extended quaternionic superspaces are constructed from the
(diffeomorphyc)graded extension of the ordinary Penrose-twistor formulation,
performed in a previous work of the authors[14], with N = p + k: These
quaternionic superspaces have 4 + k (N - k) even-quaternionic coordinates and
4N odd- quaternionic coordinates where each coordinate is a quaternion composed
by four C-felds (bosons and fermions respectively). The fields content as the
dimensionality (even and odd sectors) of these superspaces are given and
exemplified by selected physical cases. In this case the number of felds of the
supergravity is determined by the number of components of the tensor
representation of the 4-dimensional N-extended quaternionic superspaces. The
role of tensorial central charges for any N even USp (N) = Sp (N;HC) \ U (N;HC)
is elucidated from this theoretical context.
