Method contemplates: providing a set of collapsed multi-cell, crossed panel separator partitions arranged in upright position along a horizontal axis; applying vacuum grip to pull out the lead partition and move along the axis to a transfer station; relieving the pull-out vacuum grip and while supporting the partition in the upright position moving the same away from the transfer station along a second horizontal axis normal to the first axis to an opening station; applying vacuum grip to opposite sides of at least a single panel and rotating the panel to open the partition; and while the gripping force for opening is on the panel, moving the partition along a vertical axis down to an insert station and then removing the gripping force to thereby deposit the partition on the medium for which it is to serve its separating function.