  The Ramsey number $r(G)$ of a graph $G$ is the smallest integer $n$ such that
any $2$ colouring of the edges of a clique on $n$ vertices contains a
monochromatic copy of $G$. Determining the Ramsey number of $G$ is a central
problem of Ramsey theory with long and illustrious history. Despite this there
are precious few classes of graphs $G$ for which the value of $r(G)$ is known
exactly. One such family consists of large vertex disjoint unions of a fixed
graph $H$, we denote such a graph, consisting of $n$ copies of $H$ by $nH$.
This classical result was proved by Burr, Erd\H{o}s and Spencer in 1975, who
showed $r(nH)=(2|H|-\alpha(H))n+c$, for some $c=c(H)$, provided $n$ is large
enough. Since it did not follow from their arguments, Burr, Erd\H{o}s and
Spencer further asked to determine the number of copies we need to take in
order to see this long term behaviour and the value of $c$. More than $30$
years ago Burr gave a way of determining $c(H)$, which only applies when the
number of copies $n$ is triple exponential in $|H|$. In this paper we give an
essentially tight answer to this very old problem of Burr, Erd\H{o}s and
Spencer by showing that the long term behaviour occurs already when the number
of copies is single exponential.
