Semileptonic form factors D [FORMULA][FORMULA], K and B [FORMULA][FORMULA], K from a fine lattice

We extract the form factors relevant for semileptonic decays of D and B mesons from a relativistic computation on a fine lattice in the quenched approximation. The lattice spacing is a = 0.04 fm (corresponding to a -1 = 4.97 GeV), which allows us to run very close to the physical B meson mass, and to reduce the systematic errors associated with the extrapolation in terms of a heavy-quark expansion. For decays of D and D s mesons, our results for the physical form factors at [FORMULA] are as follows: [FORMULA] , [FORMULA] and [FORMULA] . Similarly, for B and B s we find [FORMULA] , [FORMULA] and [FORMULA] . We compare our results with other quenched and unquenched lattice calculations, as well as with light-cone sum rule predictions, finding good agreement.