A study on primary percolation processes taking place in a two-dimensional large-scale lattice (N×N), which represents a flat wireless sensor nano-network, has been carried out based on numerical simulations using the Monte Carlo method. The communication aspects of this nano-network, such as an average number of hops of the channel which may emerge between nodes placed on the opposite network borders, the channel integrated bit-error-probability as well as a common time of signal transfer through this channel have been investigated as well. Asymptotic dependencies of these parameters for very large network dimensions (N → ∞) have been established and determined.