Exchange composite island are the key to achieve both writeability and thermal stability in bit patterned magnetic recording. In the talk I will present micromagnetic simulations on the design of single pole write heads and media characteristics for area densities of 2.5 Tbit/in². First write fields are computed using a finite element micromagnetic solver. The head geometry is optimized for high field and high field gradient. Then these fields are used to perform switching studies of bit patterned media islands. The optimal media design was found to be an anisotropy graded media whereby the anisotropy varies quadratically with distance from the surface. I will discuss switching times and write errors. The fringing field of the write head may cause adjacent track erasure if the product of field strength and cumulative field exposure time on the adjacent track becomes to high. Based on these simulation, the relation between bit error rate and thermal stability is discussed. The results show a linear trade off between bit error rate and thermal stability.