  The family of quaternionic quasi-unitary (or quaternionic unitary
Cayley--Klein algebras) is described in a unified setting. This family includes
the simple algebras sp(N+1) and sp(p,q) in the Cartan series C_{N+1}, as well
as many non-semisimple real Lie algebras which can be obtained from these
simple algebras by particular contractions. The algebras in this family are
realized here in relation with the groups of isometries of quaternionic
hermitian spaces of constant holomorphic curvature. This common framework
allows to perform the study of many properties for all these Lie algebras
simultaneously. In this paper the central extensions for all quasi-simple Lie
algebras of the quaternionic unitary Cayley--Klein family are completely
determined in arbitrary dimension. It is shown that the second cohomology group
is trivial for any Lie algebra of this family no matter of its dimension.
