  Let $G$ be a graph in which each vertex initially has weight 1. In each step,
the weight from a vertex $u$ to a neighbouring vertex $v$ can be moved,
provided that the weight on $v$ is at least as large as the weight on $u$. The
total acquisition number of $G$, denoted by $a_t(G)$, is the minimum
cardinality of the set of vertices with positive weight at the end of the
process. In this paper, we investigate random geometric graphs $G(n,r)$ with
$n$ vertices distributed u.a.r. in $[0,\sqrt{n}]^2$ and two vertices being
adjacent if and only if their distance is at most $r$. We show that
asymptotically almost surely $a_t(G(n,r)) = \Theta( n / (r \lg r)^2)$ for the
whole range of $r=r_n \ge 1$ such that $r \lg r \le \sqrt{n}$. By monotonicity,
asymptotically almost surely $a_t(G(n,r)) = \Theta(n)$ if $r < 1$, and
$a_t(G(n,r)) = \Theta(1)$ if $r \lg r > \sqrt{n}$.
