Percolation at a surface: scaling theory and the real space renormalisation group

Scaling theory is derived for the ordinary, extraordinary and surface transitions in percolation processes at a surface and 'special plane'. The scaling theory is supplemented by the results of the real space renormalisation group for square and cubic lattices. In addition it is shown that the single cell RSRG is consistent with a crossover exponent phi =1- nu for the special plane problem (for all sizes of cell).