In this paper we investigate radial and tangential limits of pluri-Green potentialsVμon the unit ballBin, which for suitableμare defined bywhere forzεB,φzdenotes the holomorphic automorphism ofBsatisfying φz(0)=z, φz(z) = 0, and φz(φz(w))=w. The main result of this paper is as follows: Let λ be theM-invariant measure onBand letfbe a non-negative measurable function onBsatisfying, andfor somep<1, then the pluri-Green potentialVfhas tangential limit at almost all points of the boundarySofB. It is shown that the result is best possible.