I have come across sums where initially some capacitors are connected to a battery. The individual capacitances and voltage are given. The battery is then removed and the capacitors are again connected. We are to find the final charges on each and the voltage through each.

What is the theory behind solving such problems?

see juana i am not sure.but i think that whencapacitors are connected again then they must be possessing some potential difference and charges indivisually.so hence when they are connected pottential diff. across them will be=highest pot. diff. of 1 capacitor - lowest pot diff of other  capacitor.charge can be found depending on combinations.

The presence of the battery constrains the potentials of certain points in the circuit to be constant. If a bettery isn't there, then the potentials of points in the circuit redistribute owing to charge redistribution. See HC Verma solved examples ... there are such problems there.

When the capacitors are again connected,they attain a common potential V=C₁V₁+C₂V₂/C₁+C₂,where V₁,V₂ are potentialdifferences across them initially.