HOMER has a default 'Carbon content' of 88 (% by mass) for diesel.  The petrol company gave me the following spec. on their carbon content: "Carbon content as determined by carbon residue test is <0.1 wt%".   Why such a large discrepancy?  Is HOMER asking for a different parameter than what I got from the petrol company?

Good question.  Yes, I think they are referring to something different, unless that is some intergalactic carbon-free kind of diesel fuel that I have never heard of.

They might be referring to the quantity of solid carbon in the fuel.  That would be a contaminant, and I imagine diesel fuel would contain a small amount of it, maybe on the order of 0.1% but I would have guessed less than that.

But that's not what HOMER wants to know.  The 'carbon content' in HOMER refers to the fraction of the mass of the fuel that is actually carbon atoms.  In hydrocarbon fuels, that is two-thirds or higher.

Methane has the lowest carbon fraction: it consists of four hydrogen atoms (molecular mass 1) and one carbon atom (molecular mass 12), so the carbon fraction is 12 / 16 = 67%.  Cetane, a principal constituent of diesel fuel, is C16H34, so its carbon fraction is 192 / 226 = 85%.  Diesel fuel is a stew of ingredients, varying from place to place and according to time of year in cold climates.  But a broad average carbon content of 88% is about right.