Question
i have 3 broom plants that i would like to transplant. i understand the bigger the plant the harder it is to move these plants. when can they be moved with the best results.

Answer
Hi Daniel,
Thanx for your question.  Yes, the bigger the plant the more difficult it is to move.  For best results, transplant your brooms when you know you have at least 45 days before the first frost.  I don't know you location so assuming a general location in the temperate U.S., I'm going to say late August or early September.  The alternative time which is equally a good time is in the spring right after the last frost.  I hope this helps.
Tom