  The much debated issue of the transverse single spin asymmetry A_N observed
in the inclusive large P_T production of a single hadron in pp interactions,
p(transv. polarized) p --> pion X, is considered in a TMD factorization scheme.
A previous result [1,2] stating that the maximum contribution of the Collins
effect is strongly suppressed, is revisited, correcting a numerical error. New
estimates are given, adopting the Collins functions recently extracted from
SIDIS and e+e- data, and phenomenological consequences are discussed.
