If your Agapanthus are a particular variety, the plants the seeds produce will not be the same variety - if you want the same variety, better to split the plant.

Agapanthus seeds shouldn't be sown till spring, see here under Propagation

https://www.rhs.org.uk/advice/profile?PID=60

Sow the seed fresh. It germinates better straight from the plant rather than being dried off.
Cover lightly with grit, gravel or whatever rather than compost.
Sow in a deep pot rather than a seed tray (reasons later).
Leave exposed to weather. They need a period of cold followed by warmth to initiate germination.
When (if?) they germinate do not be in a hurry to p rick them out. This is the reason for deep pot rather than seed tray. They have only one root to begin with and if it is damage, it dies and a new one has to be produced from the base of the seedling. usually they die.
Feed the seed pot with dilute Baby Bio type stuff, until the leaves go yellow then allow the pot to dry off.
Repotting may be done when they are dormant. Some types never really go dormant so be careful.
I often do not repot until they have had another seasons growth.

Sorry Bamboo, but I have never managed to get dried Agapanthus seeds to germinate, even when kept properly dried over winter.

No need for apology - I've never grown them from seed, I was just passing on RHS advice, not speaking from experience, I always just divide them. Interesting to hear your experience...

Got a lovely dwarf form flowering this year from seed sown about three years ago, straight from the plant (via a drive home with a pocket full of seed).