Euonymus. This thread may be helpful. http://forums.gardenweb.com/forums/load/pests/msg0817290317765.html

Thanks, Bob. Zelkova serrata (Japanese zelkova) looks like a close match. The branch angles and bark description fit, but there may be differences in the leaf and twig description. Some descriptions online say Zelkova serrata should have acuminate leaf shape, and I wonder if this mystery tree has leaves pointy enough for that description. Also, the Zelkova serrata twig is described as brown and zigzag, while the mystery tree has gray, straight twigs. I've attached a new photo from a branch that may show more detail. (Also, as a side note, I learnt a new word today: lenticels. Great word!)

Looks a lot like a vine called Virginia Creeper, used in landscapes. Makes a very nice vine on walls or trellises. The leaves turn a beautiful red in the fall, then goes dormant for the winter. It grows an extensive root system and is very difficult to get rid of once well established. However, if you use some full strength glyphosate, not the ready-to-use mix but the stuff that is 40% or more active ingredient, you can use a cotton glove or paintbrush or sponge and coat new sprouts when they come out of the ground. This allows you to miss getting your holly by accident, and it will take the vine out but may need a couple applications as regrowth appears. The Roundup won't hurt the holly as long as you don't get any on the holly leaves even though their roots are close together. Your other alternative is to continue doing what you are doing now--keep cutting it off everytime some growth appears out of the ground to prevent any photosynthesis and gradually starve the roots out.

Hello Ken, Yes, I like to sterilize potting-mixes too. I make my own blend. Mostly peat, harvested sand and some biochar and (sorry) "twist of lime". The sand is important as it gives good drainage AND weight to the pot. Tiffany and Gardengal, I know IDing plants can difficult and posting pictures are often the simplest way to ID plants. (I guess I posted the picture twice.) I am interested in what exactly this plant is and any available on-line plant ID sites. Thank you! Doug