Car:  1990 Honda Civic LX, 5-speed, 1.5L SOHC DPFI.

Question:  Can anyone explain, or point me to a site that explains, the
exact functions the main relay is responsible for?

Here is the reason why I ask.  My main relay is screwed up, because it
will not start when it's hot.  I have to reach down and squeeze the crap
out of it while pressing the clutch and turning the key for my engine to
fire.  (Yes, I have unbolted the relay from its original position and
have it dangling beneath my dash.  Otherwise, I couldn't drive my car
anywhere)  Once I do get the car to start, while it does run, it
sputters when idling.  (The "rhythm" of the sputter is quite irregular)
 The power curve is very erratic.  Between 1k-2k RPMs, acceleration is
very sluggish, (even in 1st gear) almost like I have a fouled plug.
(That's not the issue, the plugs and wires are all brand-new)  Once I
pass 2k, there is a surge of power, then at 5k, another surge of power.
 Kind of a nifty effect, but I know it's not supposed to do that.  I
recently replaced my distributor, and the timing is set right in the
middle.  (I have no timing light to set it exactly)  Regardless of how I
set the timing, the sputtering is still present, so I've pretty much
ruled it out as the cause.  I'm using Bosch Platinum "+4" spark plugs,
and Autolite Ignition #86472 plug wires.  All engine components and
other parts are stock, with the exception of an air-intake (metal pipe
with cone filter) and a DynoMax muffler with 2¼" exhaust pipe.

Thanks in advance for any info!

Jonathan