Each sucker is a new plant and takes energy to grow and produce fruit. When you take the suckers off your tomato plants you are giving the mother plant a boost in energy and at the same time creating a new tomato plant.
Make sure the sucker is about 5 to 6 inches tall before you remove it. This size seems to take hold quicker when planted. You can pinch or cut it off. It will look like a tomato plant without roots.
Bury it in the soil up to the top leaves and water. After the first few hours it will wilt. Don't be tempted to pull it out!! After several days it will "perk up" and as the root system takes hold it will become stronger and begin to grow.
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I have done this for several years and the tomatoes on the sucker plant have been just as tasty as the mother plant tomatoes. This is a great way to have several similar tomato plants without the cost and they will mature later so your tomatoes just keep coming!
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Happy Gardening!