  We consider tripartite entangled states for continuous variable systems of
EPR type, which generalise the famous bipartite CV EPR states (eigenvectors of
conjugate choices X1 - X2, P1+ P2, of the systems' relative position and total
momentum variables). We give the regularised forms of such tripartite EPR
states in second-quantised formulation, and derive their Wigner functions. This
is directly compared with the established NOPA-like states from quantum optics.
Whereas the multipartite entangled states of NOPA type have singular Wigner
functions in the limit of large squeezing, r --> infinity, or tanh r --> 1^-
(approaching the EPR states in the bipartite case), our regularised tripartite
EPR states show singular behaviour not only in the approach to the EPR-type
region (s --> 1 in our notation), but also for an additional, auxiliary regime
of the regulator (s --> \sqrt{2}). While the s -->1 limit pertains to
tripartite CV states with singular eigenstates of the relative coordinates and
remaining squeezed in the total momentum, the s --> \sqrt{2} limit yields
singular eigenstates of the total momentum, but squeezed in the relative
coordinates. Regarded as expectation values of displaced parity measurements,
the tripartite Wigner functions provide the ingredients for generalised CHSH
inequalities. Violations of the tripartite CHSH bound (B3 \le 2) are
established, with B3 ~ 2.09 in the canonical regime (s -->1^+), as well as B3 ~
2.32 in the auxiliary regime (s --> \sqrt{2^+}).
