Previous research has demonstrated that lower performance groups have a larger size-dependent cumulative advantage for receiving citations than do top-performance groups. Furthermore, regardless of performance, larger groups have less not-cited publications. Particularly for the lower performance groups, the fraction of not-cited publications decreases considerably with size. These phenomena can be explained with a model in which self-citation acts as a promotion mechanism for external citations. In this article, we show that for self-citations, similar size-dependent scaling rules apply as for citations, but generally the power law exponents are higher for self-citations as compared to citations. We also find that the fraction of self-citations is smaller for the higher performance groups, and this fraction decreases more rapidly with increasing journal impact than that for lower performance groups. An interesting novel finding is that the variance in the correlation of the number of self-citations with size is considerably less than the variance for external citations. This is a clear indication that size is a stronger determinant for self-citations than it is for external citations. Both higher and particularly lower performance groups have a size-dependent cumulative advantage for self-citations, but for the higher performance groups only in the lower impact journals and in fields with low citation density.