Jackie, I don't think it's limited to just larger stolons. I think the larger stolons are riskier for rot and blooming propagation, but thinner stolons can produce extra chicks as well. I sent someone some S. 'Jeramia' chicks this year on a trade and one of the stolons on the hen produced multiple chicks at the tip of the stolon, for example.
I think there is some chemical communication that takes place. The hen sends out the stolon with the expectation of a chick. The chick grows and takes root, eventually sending a message back to mom saying "Ok, I'm established now, I don't need nutrients from mom anymore". Mom says "OK, I'll stop sending via the stolon and the stolon dies".
When the chick doesn't get big enough to send the message (nutrients not needed) or the normal message "ok, chick here growing" disappears, mom tries to create more chicks on the stolon.
