Over-driving an ADC

Suppose we have a 10-bit unipolar ADC with a 2V reference. An analogue input voltage of 2V should give an output of 1023. What happens if the input is, say, 2.5V?
From what I've read, most ADCs plateau out and would give an output of 1023 for all input voltages in the range 2V-2.5V. Is that true of all ADCs? Or do some 'wrap-around' and give spurious lower outputs, e.g. 255, for an input in this range?

If the ADC is a "successive approximation" (which most ones built inside MCU are), then it will output 1023 for all voltages above the reference voltage.

Thanks Mike, that confirms what I read. I just wondered if some odd-ball ADCs might do things differently.

Just watch recovery time, especially if you have a cap directly on the ADC pin and the cap charges right up to Vdd.