Mosquitoes do get full after they have engorged themselves with approximately 4 or five times their own body weight in blood from a host animal.
In order to fit more and more blood and therefore nutrients into their abdomen, while mosquitoes are ingesting blood, they will periodically excrete the liquid portion of the blood in order that they can fit more of the blood solids into the body.
When their abdomen is completely filled with blood and they can take in no more, the mosquito will remove its proboscis from the skin of the animal that it is biting, and fly away.
Because of the danger involved with biting a host, as well as the difficulty in locating one, a mosquito will not stop ingesting blood until it is completely full.
