Hope I can supply a few clues, although the exact biochemical processes of ketosis has not been fully unravelled.. probably because it will not benefit the Pharmaceutical industry.
There are 2 main types of fat involved: Cholesterol and Triglycerides.
The former is a Steroid (the same basic structure as cortizone, estrogen, vitamin D, Testosterone, etc.) and is also used to make cell membranes and insulate nerves from each other, preventing \"short circuits\". It is an \"aromatic\" molecule, consisting of carbon \"rings\".
The latter is an \"aliphatic\" molecule, that is, it does not contain ring structures, but is based on Glycerol, which is practically half a blood sugar molecule: 3 carbons in a string. On each of these, there are long \"fatty acids\" which is why we call them Tri (3) Glycer (ol) Ides.. When these are needed for energy, the Glycerol is parted from the fatty acids, and 2 of them pair up to make blood sugar (glucose). The fatty acids is turned into Ketones and yes, the liver can do so quite effectively but there is a lot of evidence that other cells in the body also has this ability. In people who haven't fasted for a long time, however, the other cells may have \"forgotten\" how to (their relevant enzymes are not active) which is why most are made in the liver during experiments.
Any good Biochemistry book should explain the processes in detail although many don't simply because it is considered irrelevant in disease based \"health care\".
André