Regularity and irreducibility of linear systems of plane curves passing through points in P^2 in general position, with given multiplicity

Given any s points P1,....,Ps in the projective plane and s positive integers m1,...,ms, let S_n be the linear system of plane curves of degree n through the Pi's with multiplicity at least mi. When the Pi's are in general position, i.e. no three of them on a line, we give numerical criteria to the effect that S_n be regular and/or irreducible