and

Let P (n,M) be a graph chosen uniformly at random from the family of all labeled planar graphs with n vertices and M edges. In the paper we study the component structure of P (n,M). Combining counting arguments with analytic techniques, we show that there are two critical periods in the evolution of P (n,M). The first one, of width Θ(n2/3), is analogous to the phase transition observed in the standard random graph models and takes place for M = n/2 +O(n2/3), when the largest complex component is formed. Then, for M = n + O(n3/5), when the complex components cover nearly all vertices, the second critical period of width n3/5 occurs. Starting from that moment increasing of M mostly affects the density of the complex components, not its size.