  In critical percolation models, in a large cube there will typically be more
than one cluster of comparable diameter. In 2D, the probability of $k>>1$
spanning clusters is of the order $e^{-\alpha k^{2}}$. In dimensions d>6, when
$\eta = 0$ the spanning clusters proliferate: for $L\to \infty$ the spanning
probability tends to one, and there typically are $ \approx L^{d-6}$ spanning
clusters of size comparable to $|\C_{max}| \approx L^4$. The rigorous results
confirm a generally accepted picture for d>6, but also correct some
misconceptions concerning the uniqueness of the dominant cluster. We
distinguish between two related concepts: the Incipient Infinite Cluster, which
is unique partly due to its construction, and the Incipient Spanning Clusters,
which are not. The scaling limits of the ISC show interesting differences
between low (d=2) and high dimensions. In the latter case (d>6 ?) we find
indication that the double limit: infinite volume and zero lattice spacing,
when properly defined would exhibit both percolation at the critical state and
infinitely many infinite clusters.
