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In a series circuit, the tail of one component is connected to the head of another component, and so on. The current flowing through this pattern is the same for all the components.

In a parallel circuit, all the heads are connected and tails are connected and the potential drop across all the components is the same.

As shown in the figure, the middle branch and bottom one are in parallel, so they have the same voltage. Therefore, the voltage across bulb A equals the combined voltage of bulbs B and C. Hence, bulb A has the greatest voltage and the greatest brightness

If A is unscrewed, the voltage will be the same for C and B because they are connected in parallel with bulb A, therefore they have the same brightness even after A is removed.

If B is unscrewed, bulb A has the same brightness because the voltage across A does not change due to the parallel connection. While for C, it is in series with bulb B, so when B is unscrewed, there is no current across the bottom branch and bulb B will switches off.

If C is unscrewed, the same thing occurs as when B is unscrewed. Bulb A has the same brightness, but bulb B will switch off.

Thus, Bulb A has the greatest voltage, hence the greatest brightness. If A is unscrewed, bulbs B and C have the same brightness. If B is unscrewed, bulb A has the same brightness while bulb C switches off. If C is unscrewed, bulb A has the same brightness while bulb B switches off.