  Let G be a group. We say that G has spread r if for any set of distinct
non-trivial elements {x1,...,xr}\subset G there exists an element y\in G with
the property that <xi, y> = G for every 1 0<i<r+1. The group G has exact spread
r if it has spread r but not r + 1. The case where G is a finite simple group
is particularly interesting since it is known that in this case the spread is
at least 2. The precise value of the exact spread of a simple group is known in
very few cases. Here we determine the precise value of the exact spread in the
smallest sporadic group for which this is still unknown, the Mathieu group M12.
