Context : Extremely metal-poor ( EMP ) stars in the halo of the Galaxy are sensitive probes of the production of the first heavy elements and the efficiency of mixing in the early interstellar medium .
The heaviest measurable elements in such stars are our main guides to understanding the nature and astrophysical site ( s ) of early neutron-capture nucleosynthesis .

Aims : Our aim is to measure accurate , homogeneous neutron-capture element abundances for the sample of 32 EMP giant stars studied earlier in this series , including 22 stars with [ Fe/H ] < - 3.0 .

Methods : Based on high-resolution , high S/N spectra from the ESO VLT/UVES , 1D , LTE model atmospheres , and synthetic spectrum fits , we determine abundances or upper limits for the 16 elements Sr , Y , Zr , Ba , La , Ce , Pr , Nd , Sm , Eu , Gd , Dy , Ho , Er , Tm , and Yb in all stars .

Results : As found earlier , [ Sr/Fe ] , [ Y/Fe ] , [ Zr/Fe ] and [ Ba/Fe ] are below Solar in the EMP stars , with very large scatter .
However , we find a tight anti-correlation of [ Sr/Ba ] , [ Y/Ba ] , and [ Zr/Ba ] with [ Ba/H ] for -4.5 < [ Ba/H ] < -2.5 , also when subtracting the contribution of the main r -process as measured by [ Ba/H ] .
Spectra of even higher S/N ratio are needed to confirm and extend these results below [ Fe/H ] \simeq - 3.5 .
The huge , well-characterised scatter of the [ n-capture/Fe ] ratios in our EMP stars is in stark contrast to the negligible dispersion in the [ \alpha /Fe ] and [ Fe-peak/Fe ] ratios for the same stars found in Paper V .

Conclusions : These results demonstrate that a second ( “ weak ” or LEPP ) r -process dominates the production of the lighter neutron-capture elements for [ Ba/H ] < -2.5 .
The combination of very consistent [ \alpha /Fe ] and erratic [ n-capture/Fe ] ratios indicates that inhomogeneous models for the early evolution of the halo are needed .
Our accurate data provide strong constraints on future models of the production and mixing of the heavy elements in the early Galaxy .