Planting tomatoes: Vertical vs. Horizontal

I used to always plant my tomatoes vertically. Dig a really deep hole, hold the plant upright and fill in the hole leaving the top few inches exposed.

For years now, I've been planting them in a shallow trench. Dig the trench 4 or 5 inches deep, lay your plant horizontal and curl the top upwards leaving the top few inches exposed.

The reason for the horizontal planting was:
*Easier to dig shallow trench than a deep hole
*Plant has access to rainwater if it only wet the first couple inches
*The soil at that level should be warmer
*Both methods would produce roots all along buried stalk

What may make vertical planting the better choice? I've wondered:
*Could the deeper roots have access to ground water that trenched plants couldn't reach?
*Are there more available nutrients at a deeper level?
*Is shallow trenching putting the plant at risk of drying out? Roots getting too hot?

I grow mine in rows (not permie, I know), tied to strands of string supported by t-posts and mulched with whatever I can find (leaves, grass, alfalfa, straw...)

What do you do, and why?

My biggest problem with laying plants in the ground horizontally is that I forget that I've done that, and then when I'm weeding I chop the roots off. I tried replanting the carrot root crop horizontally one year. Oops. I pulled more than a few carrots out of the ground with my hoe.

Waking this thread back up. Last fall I found volunteer tomatoes out where I had given the chickens some really good heirloom tomatoes that had gone bad. I potted them up, brought them in, put them under a grow light that sits over 6 feet off the floor. At this point they are past leggy, I don't know what to call them. The tallest one, if it was stretched out, is probably 9 feet tall, with leaves every foot or so. The others are about 5 or 6 feet tall, with the same sparse leaves. If I trench plant them, do I need to remove all their leaves? They root all along, like a squash, correct? So if I plant them so their bare sections are allowed to root, leaving the leaves up, will I get what looks like a separate plant every foot or so where the leaves are? I am visualizing them looking like a sea serpent when planted.

Pearl Sutton wrote:will I get what looks like a separate plant every foot or so where the leaves are? I am visualizing them looking like a sea serpent when planted.

As would I. A new shoot emerging at each exposed leaf node.