Eearlier in the year I was given 40 basil seeds. They were scattered on potting compost and covered with cling film. After a short time they 'all' germinated. 10 were potted on into 5" pots and the rest were given away.
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They have since developed into small trees and smell amazing when watered. They have stayed in my polytunnel and get watered evey day.
It sems they are a small leafed version and have all the benefits of the larger beter known version available from any supermarket.
My guess is your wilting will have come from transplanting too soon before the seedling has developed enough.