  We give a complete description of the congruences on the partition monoid
$P_X$ and the partial Brauer monoid $PB_X$, where $X$ is an arbitrary infinite
set, and also of the lattices formed by all such congruences. Our results
complement those from a recent article of East, Mitchell, Ruskuc and Torpey,
which deals with the finite case. As a consequence of our classification
result, we show that the congruence lattices of $P_X$ and $PB_X$ are isomorphic
to each other, and are distributive and well quasi-ordered. We also calculate
the smallest number of pairs of partitions required to generate any congruence;
when this number is infinite, it depends on the cofinality of certain limit
cardinals.
