Tarragon Propagation

I live in southern Colorado, USA and started an herb garden last year. I planted two tarragon plants; they did pretty well. Now I notice that all kinds of little tarragon plants are starting to come up around the two I planted. Can you tell me how I can start new plants from these so I can share with friends and family? Any help you can give me will be appreciated.

If you planted true french tarragon plants then the little plants can only be offshoots from the parent plant, since french tarragon is sterile [incapable of producing seeds]. In the early spring check that the plants are connected to the parent by an underground stem. If they are, then you can make new plants by cutting the connection with a sharp spade and lifting the plantlet with some attached soil and pot them up for transport to your friends.
If there is no connection, then chances are good that the plant was not french tarragon, but russian tarragon and these are seedlings that may or may not have any taste. You will have to check the taste of each one and decide if it is worthwhile to keep. Their taste won't be as strong as that of the french variety, but by using a lot, you can still make tarragon vinegar from it.