Question
when and how should agapanthae be divided -  

Answer
I have to tell you the truth: I do not know what I "should" have done.

What I have done, whether it is the right thing or not, has been quite successful.  I divide in the spring when growth begins.  If the pot contains more bulbs than roots, that is a good indication to act.  I found it very difficult to tease the bulbs apart (I probably waited too long) so I actually took a knife to the clump and cut it into several pieces with at least three bulbs each.  Yes, you lose a few bulbs this way, but when you have a full pot, that leaves plenty.  You may lose a year's bloom when dividing if it is too traumatic for the plant.  Plant the divisions in containers that you expect them to fill in three years.  Agapanthus likes to be somewhat crowded in a container, so it does not pay to use a pot that is much too large.  

Use an all-purpose potting mix such as ProMix and add slow-release fertilizer (Osmocote is one).  The rate of release should match your growing season.  Overfertilizing (with high nitrogen fertilizer) promotes foliar growth at the expense of flowers.  I use 14-14-14.