Let P(n,m) be a graph chosen uniformly at random from the class of all planar graphs on vertex set {1,... ,n} with m = m(n) edges. We study the cycle and block structure of P(n,m) when m ∼ n/2. More precisely, we determine the asymptotic order of the length of the longest and shortest cycle in P(n,m) in the critical range when m = n/2 + o(n). In addition, we describe the block structure of P(n,m) in the weakly supercritical regime when(a) If s 3 n −2 → −∞, then whp L 1 is a tree and c (R) = Θ p n|s| −1 .

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