Thanks! But if someone has very little fat tissue, where does the anesthetic go after it leaves the target organs? Would this cause a relative increase in potency in a very lean individual?
It is important to understand diffusion, because after injection, these drugs are distributed primarily just due to their movement along concentration gradients. Likewise, their effects are terminated by re-distribution away from the site of action, again along concentration gradients.
To recap what Nova1300 said, after you inject some propofol or ketamine, the serum concentrations rise instantly. Because concentrations in the blood are very high, the drug diffuses across membranes into the CNS (their site of action) and other organs with high rates of blood flow. After those organs with the highest blood flow receive the initial distribution of the drug, the drug continues to spread out into the rest of the tissues of the body (fat, etc).
As the organs with lower blood flow "soak up" some of the drug, blood levels fall from where they were after injection. Because blood levels have now fallen, the concentration gradient is reversed away from the target tissue. Most of these drugs have relatively low affinity for their receptor targets (i.e. they aren't tightly bound to the receptors), so they quickly diffuse back towards the area of lower concentration - into the blood. At this point, elimination begins, primarily by the liver, and that is a pretty slow process. This explains how propofol can have a half-life of several hours, though it's effects only last about 10 minutes.
In theory, I think a really lean person might see a longer duration of effect, since there is less fat for the drug to distribute into, meaning that serum concentrations will take longer to fall to the point that the drug diffuses from the CNS back into the blood. But clinically, I doubt you'd really notice any more difference than the normal person-to-person variations that you always see. Maybe, though. I can't say I give propofol to many "very lean" people - usually it's the opposite.
The difference between fast acting / shorter duration drugs (fentanyl, propofol, ketamine, midazolam) and drugs that take longer to take effect and last longer (morphine, hydromorphone, diazepam, lorazepam) is primarily determined by their lipid solubility. A drug like morphine is less soluble in fat and will take longer to diffuse across the blood-brain barrier into the CNS, and will also takes longer to redistribute into other tissues and reverse the concentration gradient from blood --> target to target --> blood. It's also why on a long transport or in the ICU, intermittent boluses of morphine or dilaudid work fine, whereas if you are using fentanyl or ketamine, you either need a drip or you have to bolus much more frequently.