That "tuber" is a water storage organ & has NO possibility to produce a plant. ..... Either division or seed is the ONLY possibility.

I did do a little reading before I asked the question--I did not ask the question in a vacuum. Here are the sorts of things I found out there.

First off, it does appear that it is a true tuber--I've found this usage repeatedly in academic sources:

One example:

(this is an entry for "Asparagus sprengeri" technically both sprengeri and meyeri are correctly classified as cultivars of the same species--A. densiforus)

"Plant Characteristics: Perennial herb; roots with white tubers; sts. drooping or scrambling, 3-6 ft. long, glabrous, much branched; cladodes (flattened stem having the function of a leaf) about 1 in. long, flat, linear, straight or only slightly curved, 3-8 together, scales on main sts. spiniferous; fls. pinkish, fragrant, in loose racemes 1-3 in. long; berry somewhat 3-lobed, bright red, 1/2 in. or less diam., 1-3 seeded."

http://nathistoc.bio.uci.edu/Plants%20of%20Upper%20Newport%20Bay%20(Robert%20De%20Ruff)/Liliaceae/Asparagus%20sprengeri.htm

There are many suggestions that the tubers can give rise to plants:

"The plants have extensive root systems with fairly large tubers, which are used in nature to provide food during long periods of drought in summer. They can be readily propagated by separating the tubers in fairly large clumps, or by sowing the seed in spring or early summer."

H.G. Jamieson.
Kirstenbosch National Botanical Garden.
November 2002

http://www.plantzafrica.com/plantab/asparagdens.htm

"Asparagus Fern may be propagated by seeds and by division of the tubers."

http://edis.ifas.ufl.edu/FP052

"Bushy asparagus forms dense patches, is tough and has long-lived tubers that resprout."

http://www.biosecurity.govt.nz/pest-and-disease-response/pests-and-diseases-watchlist/bushy-asparagus

The final 3 quotes are, respectively, from Kirstenbosch Botanical Garden (I can think of no better general source of info on South African plants), the University of Florida, and the New Zealand governmental agency responsible for eradicating invasive plants.

So it's clear they are in fact tubers. The suggestion of that division into clumps of tubers can generate new plants is ambiguous--do they assume that the actual growth points are included? However the New Zealand statement does suggest that they can regrow from the tubers--are they getting sloppy in their description and in fact some growing points outside the tubers are required? Perhaps. If you've ever had these grow as weeds in your yard though, you know how they grow tubers which send out roots growing more tubers, and so on, and that the plants are nearly impossible to eradicate (where I live the sprengeri cultivar is a horrible weed). But maybe the tubers themselves are not the source--I've never directly checked.

I would admit that perhaps all of these sources are sloppy--when they say a group of tubers can give rise to new plants as a means of propagation or that plants can resprout from tubers in the ground it could in fact mean tubers plus growing point(s). I had only seen info which suggested that the plant could be propagated from a group of tubers, not just one, which is why I asked my question.

If tuber(s) alone are not capable of giving rise to a plant I would not be surprised--the descriptions above are not totally unambiguous. However the simplest interpretation of the New Zealand source does suggest tubers alone can do the job and I think at this point some sort of evidence to counter this is needed.

Happy to read that you did further research AFTER you did not like the response to your question. 3am rant? Nice.

The response was terse and inaccurate. The initial question was a valid one, which in fact I too am asking. I have attempted planting single tubers unsuccessfully. So, which way IS up? And how much of the mother plant must be kept in separating tubers? And it's not quite 5pm and I'm not ranting.