On my splitter, the wedge is stationary, and it pushes the logs out the end. The tongue on my log splitter is removable (pinned in place), so you can get it out of the way when splitting. A "kickstand" is pinned in the down position to hold up that end of the splitter when the tongue is removed.
This comes in handy when splitting right into the back of a trailer, since the splitter can push logs right into the trailer. The downside is that all the crap that piles up when using the 4-way wedge falls onto the ground right where the dolly wheel on the tongue needs to sit. The splitter weighs somewhere around 750 pounds, and there is a lot of tongue weight, so I really need the tongue in there when moving it around. I've thought of adding a receiver for the removable tongue on the back side, so I can come up to the back of the splitter to hook up and haul it away. However, the heavy tongue weight in the normal position, would probably transfer into a negative tongue weight in the rear position. I'm not sure how much of an issue that would be.