If it only shows one line leading off, it means the route is disconnected from the trade depot in some way. This could be caused by a number of things.
If you have no trade depot, it will show this. If you have a gap (even just 1 tile) in the road, it will show this. The gap can also be a single unsmoothed tile (or muddy tile) along the route to the trade depot. If you have a lot of stone on the ground still, you may need to either haul it off or go by every square slowly to ensure they are all smoothed. I had this problem before and it turned out to be a single tile in the center of my 5 wide road that the smoothing had been cancelled on somehow (I think an animal had caused one engraver to cancel a tile).
This can also be caused by raised bridges, if you have your drawbridge up the road will be blocked off and sometimes the wagons will bypass the site. Sometimes they will still show with the drawbridge up, however, so i'm not sure entirely what goes on there. The one line road will show up when you save and load after having the bridge up, or rebuild the trade depot with the bridge up. It won't show all 3 tiles leading off again until you rebuild the depo with the bridge down or save/load with the bridge down.
One easy way to determine if it was a unsmoothed tile is to rebuild the depot closer to the edge of the map and see if the road shows up correctly, then you can progressively build it closer to where you want it until you isolate where the problem is.
I have also found that trees off the edge of the map DO NOT affect the road. If you can't cut them, they are off the map and will not stop the road. I had thought this myself on one occasion, and it caused me a lot of hassle, until I finally realised that lo and behold it was a single muddy tile on the way to the river. Once I built a bridge over that one tile (and then destroyed and rebuilt the depot to get it to re-check for road) it showed up correctly, even with the tree.