  The biased link occupation rule in the Achlioptas process (AP) discourages
the large clusters to grow much ahead of others and encourages faster growth of
clusters which lag behind. In this paper we propose a model where this tendency
is sharply reflected in the Gamma distribution of the cluster sizes, unlike the
power law distribution in AP. In this model single edges between pairs of
clusters of sizes $s_i$ and $s_j$ are occupied with a probability $\propto
(s_is_j)^{\alpha}$. The parameter $\alpha$ is continuously tunable over the
entire real axis. Numerical studies indicate that for $\alpha < \alpha_c$ the
transition is first order, $\alpha_c=0$ for square lattice and $\alpha_c=-1/2$
for random graphs. In the limits of $\alpha = -\infty, +\infty$ this model
coincides with models well established in the literature.
