Connect 3 Lithium Polymer battery with different capacity in parallel
I have seen products where 2 or more different size batteries are used in parallel. For example some Apple Macbooks have this.

If the batteries:


come from the same manufacturer
use the same chemistry
are the same "model"
are balanced (in order to have the same voltage) before connecting in parallel


so only differ in size and capacity then I think you can connect different size batteries in parallel. Then you can treat the combination as if it is one larger battery.

Then you do not need a special charging circuit, to the charging circuit the battery will behave as one larger battery.

Ideally you would consult with the battery manufacturer to confirm that this can be done.

You should NOT get some "random" batteries and combine those into one larger battery. That is asking for trouble if you ask me.