Can you identify this southern weed for me? I want to kill them without killing bermuda.?
http://i338.photobucket.com/albums/n440/bandoslav/DSC03934.jpg is a weed cluster that has started to spread out. 
http://i338.photobucket.com/albums/n440/bandoslav/DSC03944.jpg is a weed plant that has not yet spread, but about to.
http://i338.photobucket.com/albums/n440/bandoslav/DSC03938.jpg is multiple weed clusters amongst bermuda.  In the background is a border of these weeds.
http://i338.photobucket.com/albums/n440/bandoslav/DSC03937.jpg is a huge cluster of weeds let alone for a month, very tall (24") and I'm holding a seed cluster in front.  They don't seed out until they are very large.
General characteristics: very dense & moisture retaining.  Easily clogs mulching mowers.  Very fast growing, on the order of 1/2" to 1" per day.  Very tollerant of full sun to full shade, overpowers bermuda.  Roots are a thin cluster.
Location: Tennessee & Mississippi.
What doesn't kill it: Ortho weed b gone, trimec w/MSMA, Scotts weed n feed, Bayer broadleaf weed killer.
I ran out of character space to finish...
What doesn't kill these: Image lawn weed killer, Tractor Supply brand broadleaf weed killer, MSMA from local co-op.
The only way I've found to kill these is to pull up manually by the root.  Unless the soil is extremely moist (or unless there is a thick layer of mulch), the root ball will bust and the weed will regrow.  Even roundup takes multiple applications to truely kill a plant.
How they spread: Mostly by extending a long leaf and sprouting a new plant where it touches the ground.  Only neglected weeds left to grow to adulthood actually create seed stems.
The only weed I have found that can come close to competing with this weed's growth rate & spreading capacity is crabgrass...which is very easily controlled.
Growing season: all of them.  Stays green year round, but does not spread as fast during the winter months.
On the lawn service...I've used & fired Trugreen -and- Scotts lawnservice for the sole purpose being their inability to control this weed.