Do on demand hot water heaters supply you with enough hot water to run
your faucets for an hour at 120 degrees fahrenheit, without loosing
degrees in temperature, if you have 48 degree fahrenheit ground water?

Do you mean gas or electric heaters? The output of instantaneous
electric heaters is very limited.

This almost sound like a homework question. As Owain indicates,
instantaneous water heaters (gas or electric) have their limitations.
In general, they are cheaper up front to buy and install, but over a
relatively short term you lose on additional energy costs, and
capacity is limited. These systems make sense for only for situations
were the demand hot water is low or relatively infrequent.

A superinsulated tank system is the most efficient.

Yes indeed.  Here is a site that has two electric "on-demand" water heaters:

http://www.stiebel-eltron-usa.com/HTML/product_home.html

Click on the the top middle and right photos for more details, and
technical details on following pages.  Both heat to 125°F, continuous
use, require 220 volt current.

Stiebel Eltron is an excellent German maker of these heaters, perhaps
the originator of the idea. I have had one for many years.  It is
absolutely reliable.

One possible problem is deposits building up if you have hard water,
but that will be the case with any water heater of this type.

Good luck, Myoarin

Waukon,  you are wrong. They are more expensive up front, by as much
as two times. Tanks are not more efficient.  Gas heated non tank water
heaters are more efficient, as they use energy when you run hot water.
My Gas Bill is half, of my Brother's across the street ceteris
parabus...
I have a Rinaii Contiuum hot water heater, and it will provide
limitless hot water like 300GPH.

Neither storage nor instantaneous heaters are intrinsically more
efficient. It takes the same amount of energy to heat an quantity of
water by a given increase in temperature regardless of the time taken.

Storage heaters will have, even if well insulated, storage losses,
however these are *very* minor and are insignificant unless the water
use is very intermittent (eg less than within 24 hours).

Instantaneous heaters have no storage losses but can be inefficient if
small amounts of water are drawn off frequently, as the heater fires
every time the tap is opened.

Instantaneous heaters will heat water for an indefinate period of
time, but the factors are:
1. The flow rate of the incoming water mains
2. The temperature of the incoming water
3. The temperature of the outgoing water desired
4. The kW rating of the heater

What *flow* will be achieved will depend on all three factors. Whether
it is sufficient depends on your needs. You usually have no control
over 1 or 2 and little control over the maximum value of 4.

In the UK, gas instantaneous heaters (or combi boilers) are usually
adequate for a good shower, but fill a bath slowly. Electric heaters
here for domestic use are limited to about 10kW, which gives a weedy
shower (especially in winter) and is useless for filling a bath.

Owain

That is all true, but "my" Stiebel Eltron does an adequate job, and
the practical factor is that one can install an on-demand unit uneer
the sink or wherever with a minimum of plumbing work, maybe for an
addition bathroom, in a situation where it would be quite difficult to
install a big water heater and run hotwater lines.

By definition, on-demand heaters can heat continuously without losing
temperature.  They are rated at degree rise per flow rate, with lower
temp rise for higher flow rates.

Example.  75 degree rise at 3.1 gph, 65 degree rise at 4.2 gph, 40
degree rise at 7.0 gph.

So, for one faucet, I suspect you can find a unit that is capable. 
Bosch 250sk and the Takagi K-2 are the two highest capacity consumer
models.

Greg

I think my point has been proven. You can of course buy a big
on-demand unit that lets you fill the 100 gallon spa-tub without
reducing the rest of the household to a cold-water regime. But we are
speaking of normal hot-water usage, which peaks during morning-shower
time, and briefly again at wash-dinner-dishes time in most households.
We Americans also have absolute hot-water-hog washing machines (and we
Americans nearly universally also have separate dryers, vented to the
outside).

If you watch <i>This Old House</i> on US TV, you understand where I am
coming from. This TV show spends an absurd amount of money on its
renovations, but their disparagement of instantaneous hot-water
systems is correct, at least insofar as the US goes.