Ask Mr. Smarty Plants

When your question came in to Mr. Smarty Plants I was out of town and waited till I got back to town to answer it so I could go and see this plant for myself.  I drove to 6th and Nueces and, alas, it is a mess there right now because Nueces is closed for several blocks from about 6th Street to 9th Street for a construction project.  I did, however, park nearby and walked around the area a bit; but, unfortunately, couldn't find the tree you referred to or the ground cover underneath it.  I didn't try the Gracywoods area since you didn't list any specific locations there.

I very seriously doubt if the ground cover is an Ilex species.   The only common ones found in the Austin area are Ilex vomitoria (Yaupon) and Ilex decidua (Possumhaw) and neither of these have leaves that are a prickly holly shape, i.e., similar to Ilex opaca (American holly).  There are two plants native to the area that have holly-like leaves, Mahonia trifoliolata (Agarita) and Mahonia swaseyi (Texas barberry) but neither of those really matches your description either. 

What your description sounds like to me are root sprouts of the live oak Quercus fusiformis (Escarpment live oak).  There are several reasons I say this:  1) they are not easily dug up since they grow from the tree root; 2)  they don't flower; 3)  they are evergreen; 4) they get their water from the roots of the tree itself and 5)  they have pointed lobes on their leaves that make them look like holly leaves (see the statement on their species page):

"Leaves are evergreen, firm textured, ovate to elliptic, 1 to 3 inches long; usually without lobes except on young plants and rootsprouts, then with pointed lobes." 

Here is a photo of a leaf of Q. fusiformis and scroll down this page from Catnapin to find more pictures and information about Q. fusiformis.

We  have several questions about these root sprouts because many people consider them to be a nuisance and want to get rid of them.  You can read about them in questions #6711, #6031 and #7446.

You did say in your question that they aren't oak seedlings and I don't think they are seedlings either; but I do think that they are most likely root sprouts from the tree they are growing under.

If you feel doubtful that they are root sprouts, you can take photos of them and then visit our Plant Identification page where you can find links to several plant identification forums that accept photos of plants for identification.