I replaced mine this afternoon, along with a wishbone, and inner CV boot. Been in the trade 20 odd years and never used a ball joint splitter yet. Take the nut right off from the track rod end, and give the side of the "eye" where the track rod end thread goes through a good square smack with a hammer, you really shouldn't need to do this more than twice....the track rod end will jump out.
If you try the other method of leaving the nut on a few threads, and then freeing the joint, you'll be left with the nut on a free spinning joint which can cause a few headaches if you don't have air tools as its not easy to hold the joint whilst undoing the nut. If this does happen, use a long lever to put downward pressure on the top of the track rod end while undoing the nut.
Best to slacken the locknut on the other end first while its held in place, use a bit of heat if needed.
Remember, after April, split boots on balljoints and track rod ends will be an MOT failure- fork type ball joint splitters almost always split the boot.