  We present a new and very high statistics study of D and D_s semileptonic
decay form factors on the lattice. We work with MILC N_f=2+1 lattices and use
the Highly Improved Staggered Action (HISQ) for both the charm and the light
valence quarks. We use both scalar and vector currents to determine the form
factors f_0(q^2) and f_+(q^2) for a range of D and D_s form factors including
those for D to pi and D to K semileptonic decays. By using a phased boundary
condition we are able to tune accurately to q^2=0. We also compare the shape in
q^2 to that from experiment. We show that the form factors are very insensitive
to the spectator quark: D to K and D_s to eta_s form factors are essentially
the same, and the same is true for D to pi and D_s to K. This has important
implications when considering the corresponding B/B_s processes.
