We explore the formation and relaxation of so-called quasi-stationary states (QSS) for particle distributions in three dimensions interacting via an attractive radial pair potential V(r→∞)∼1/rγ with γ>0, and either a soft-core or hard-core regularization at small r. In the first part of the paper we generalize, for any spatial dimension d≥2, Chandrasekhar's approach for the case of gravity to obtain analytic estimates of the rate of collisional relaxation due to two body collisions. The resultant relaxation rates indicate an essential qualitative difference depending on the integrability of the pair force at large distances: for γ>d−1 the rate diverges in the large particle number N (mean field) limit, unless a sufficiently large soft core is present; for γ