  In this paper, we address several Erd\H os--Ko--Rado type questions for
families of partitions. Two partitions of $[n]$ are {\it $t$-intersecting} if
they share at least $t$ parts, and are {\it partially $t$-intersecting} if some
of their parts intersect in at least $t$ elements. The question of what is the
largest family of pairwise $t$-intersecting partitions was studied for several
classes of partitions: Peter Erd\H os and Sz\'ekely studied partitions of $[n]$
into $\ell$ parts of unrestricted size; Ku and Renshaw studied unrestricted
partitions of $[n]$; Meagher and Moura, and then Godsil and Meagher studied
partitions into $\ell$ parts of equal size. We improve and generalize the
results proved by these authors. Meagher and Moura, following the work of Erd\H
os and Sz\'ekely, introduced the notion of partially $t$-intersecting
partitions, and conjectured, what should be the largest partially
$t$-intersecting family of partitions into $\ell$ parts of equal size $k$. The
main result of this paper is the proof of their conjecture for all $t, k$,
provided $\ell$ is sufficiently large. All our results are applications of the
spread approximation technique, introduced by Zakharov and the author. In order
to use it, we need to refine some of the theorems from the original paper. As a
byproduct, this makes the present paper a self-contained presentation of the
spread approximation technique for $t$-intersecting problems.
