We study the s-process abundances (A>~90) at the epoch of the solar system formation. Asymptotic giant branch yields are computed with an updated neutron capture network and updated initial solar abundances. We confirm our previous results obtained with a Galactic chemical evolution (GCE) model: (1) as suggested by the s-process spread observed in disk stars and in presolar meteoritic SiC grains, a weighted average of s-process strengths is needed to reproduce the solar s distribution of isotopes with A>130; and (2) an additional contribution (of about 25%) is required in order to represent the solar s-process abundances of isotopes from A=90 to 130. Furthermore, we investigate the effect of different internal structures of the ^13^C pocket, which may affect the efficiency of the ^13^C({alpha},n)^16^O reaction, the major neutron source of the s process. First, keeping the same ^13^C profile adopted so far, we modify by a factor of two the mass involved in the pocket; second, we assume a flat ^13^C profile in the pocket, and we test again the effects of the variation of the mass of the pocket. We find that GCE s predictions at the epoch of the solar system formation marginally depend on the size and shape of the ^13^C pocket once a different weighted range of ^13^C-pocket strengths is assumed. We obtain that, independently of the internal structure of the ^13^C pocket, the missing solar system s-process contribution in the range from A=90 to 130 remains essentially the same.