To put it in a few words: maritime city-states (MCS) would give 1:friend/2:ally food per era, distributed among all cities, with each city's allocation based on its population and status (puppet, capital, etc).
For example, if we have a 10

and 5

city, the first would get twice as much MCS food as the second because it's twice the population. If the 10

city is being razed, food that would normally go there it is distributed among other cities in the empire.
Does this make more sense?
Here's another example... say we have:
- 10
from MCS
- 5
capital
- 10
city
connected to the capital
- 10
city not connected
The food to each would be:
- 4
to capital
- 4
to connected city
- 2
to not-connected city
This is because the capital acts as a city twice its size (200% multiplier), while the non-connected city acts as one half its size (50%).
These would be the multipliers:
000% -

Razing
050% -

Puppet
100% -

Occupied
200% - Resistance (avoid starvation)
200% -

Capital
050% - Not

connected to Capital
050% - Blockaded
00X% - "Avoid Growth" button checked (0% food if less than <80% of the empire is on avoid status)
So in other words, puppets get half as much MCS food, while capitals get twice as much, and cities on 'avoid growth' would generally get no MCS food. If a city gets less food it's sent elsewhere in the empire, and vice versa. The total amount of food to the entire empire would always be a fixed, unchanging number based on era and number of MCS friends/allies.