The recording physics of bit patterned media is studied for areal densities of around 2 Tbits/inch2, focused on number of grains per bit. Write error rate and signal to noise ratio in a function of number of grains are derived as analytical functions based on the statistics theory on the binomial distribution. Modeling of writing process based on the head field gradient and switching field distribution and interference fields, is presented to extract the write-head and media parameters which are necessary to attain a high areal density recording. ©The Electrochemical Society.