  On the basis of the Usadel equation we study a multi-terminal Josephson
junction. This junction is composed by "magnetic" superconductors
S$_{\text{m}}$ which have singlet pairing and are separated from the normal
n~wire by spin filters so that the Josephson coupling is caused only by fully
polarized triplet components. We show that there is no interaction between
triplet Cooper pairs with antiparallel total spin orientations. The presence of
an additional singlet superconductor S attached to the n wire leads to a finite
Josephson current $I_{\text{Q}}$ with an unusual current--phase relation. The
density of states in the n wire for different orientations of spins of Cooper
pairs is calculated. We derive a general formula for the current $I_{\text{Q}}$
in a multi-terminal Josephson contact and apply this formula for analysis of
two four-terminal Josephson junctions of different structures. It is shown in
particular that both the "nematic" and the "magnetic" cases can be realized in
these junctions. In a two-terminal structure with parallel filter orientations
and in a three-terminal structure with antiparallel filter orientations of the
"magnetic" superconductors with attached additional singlet superconductor, we
find a nonmonotonic temperature dependence of the critical current. Also, in
these structures, the critical current shows a Riedel peak like dependence on
the exchange field in the "magnetic" superconductors. Although there is no
current through the S/n interface due to orthogonality of the singlet and
triplet components, the phase of the order parameter in the superconuctor S is
shown to affect the Josephson current in a multi-terminal structure.
