The standard explanation is dirt (or soot from candles) in the rooms
accumulates around the registers due to airflow as show in the diagram
here about 1/3 of the way down, where it says "Dirt on the ceiling":

http://hphaa.com/editorials/index.htm#sky

The gal who lives in the apartment keeps it quite clean. She regularly
burns candles (mostly the expensive Yankee brand) and has been doing so
for over nine years. The soot problem just started about four days ago.
She hasn't switched brands or even started burning new candles from the
same company. Also, while the soot is most visible against the white
ceilings within six or so inches from the registers, cups just sitting
on counters about 30" above the floor are also coated with soot/dirt.

She keeps the wicks trimmed. I guess it's possible that the bottom of a
wick has a defect that only shows up as the upper portion of the candle
burns away, but there hasn't been visible smoke.

Last Saturday, the smoke alarm went off in her apartment. Couldn't tie
it directly to the candles, but after she put them (four or so) out, the
alarm stopped.

The problem is most intense in the kitchen, which also happens to be the
closest room to the gas furnace located in the attic above her kitchen.
The more distant the register, the less noticeable the soot. (Also, no
candle burning in the distant room.)

The furnace is about nine years old, so a leak in the air exchanger is
unlikely. Even if there is one, there also would have to be incomplete
combustion of the gas to allow carbon particles to mix in the heated air
to her apartment.

Thanks for your ideas.

R1