Density profile of the incipient infinite percolation cluster

Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance fro m the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact r esults in d = 2 and d = 6 - epsilon dimensions and with earlier simulations . We also present and explain results for bus-bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of th e samples.