Kirchhoff's Junction Rule

The junction rule states that the current arriving at a node equals the current leaving it, which fixes the total and nothing else. Each branch's share follows from the potential difference the parallel branches have in common and that branch's own resistance, $I_k = \Delta V/R_k$, so the current divides in inverse proportion to the resistances and the larger share goes to the smaller one. Removing a branch raises the equivalent resistance, lowers the total current and redistributes every potential difference in the circuit, so a mixed circuit has to be solved again from the top.

Two errors dominate. Halving the current at every branch point regardless of what the branches contain, which conserves charge and still gets both branch currents wrong except when the branches happen to be equal. And assuming the rest of a circuit keeps its old currents and brightnesses when one bulb burns out, when in a mixed circuit a single removal routinely dims some bulbs while brightening others.