  We investigate a random--neighbours version of the two dimensional
non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev.
Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that
criticality can be expected even in the presence of dissipation. As the
critical level of conservation, $\alpha_c$, is approached, the cut--off of the
avalanche size distribution scales as $\xi\sim(\alpha_c-\alpha)^{-3/2}$. The
transition from non-SOC to SOC behaviour is controlled by the average branching
ratio $\sigma$ of an avalanche, which can thus be regarded as an order
parameter of the system. The relevance of the results are discussed in
connection to the nearest-neighbours OFC model (in particular we analyse the
relevance of synchronization in the latter).
