We present a simple algorithm that produces a so called Ramified Random Apollonian Networks (R-RAN) in any dimension. Analytical derivations show that these networks still exhibit small-word and scale-free characteristics. To characterize further the structure of R-RAN, we introduce new parameters that we refer to as the parallel degree and the ramification coefficient, that determine locally and in average the number of vertices inside the (d+1)-cliques composing the network. We provide analytical derivations for the computation of the degree and parallel degree distributions, ramification and clustering coefficients and the average path lengths for R-RAN. We finally show that these derivations are in very good agreement with our simulations.