From time to time you might encounter a cockatiel that might lay too many eggs even if they don't have a mate.
It's very important that your cockatiel has a good source of calcium (like cuddle bone fish, commonly found in pet stores) , plenty of fresh water and even vitamin supplement for cockatiels.
During the egg laying process your cockatiel will loose important nutrients, including calcium. Eggs that are not fertile, like in the case of single female cockatiels will not hatch.
Your bird will eventually abandon the eggs at approximately 21 days, this is done just by plain instinct.
If your cockatiel continues to sit on the eggs, you can safely remove the eggs next time she gets up for a bite to eat.
If the eggs are cracked or broken, you need to remove them as soon as possible. Once they are broken they are subject to bacteria and can get your cockatiel sick.
If your cockatiel continues to lay eggs after this time frame you might want to look at other causes, like too much light. If your bird is exposed to too much light (more than 12 hours per day, artificial or natural) it will create a natural response for laying more eggs.
Certain toys including mirrors might be a cockatiels motivation to lay eggs as they might develop affection for these objects.
A diet that might be heavy on fats have been know to make your tiel lay more eggs. For example, sunflower seeds are high on fat content and they should be avoided as well as human foods like potato chips and so on. You can try giving your tiel healthy treats like low fat Cheerios, veggies and fruits.
Petting your cockatiel in a certain way can trigger egg laying too. Cockatiels in the wild will rub heads with another tiel as a mating ritual. Head rubs on your cockatiel are foreplay and signal that 'I am ready for mating.' Try to avoid rubbing your cockatiel's back as well, for a cockatiel this just feels like mating.
Most birds have a natural instinct for 'nesting'. Make sure that you do not have any nesting materials around the cage that might trigger your cockatiel's natural call for making a nest and lying eggs. Nesting materials are things like paper, natural fibers or small pieces of wood.
It's important that you visit your avian vet if this problem continues.
As always the information offered here is to provide guidance and is not intended to be a substitute for the good advice provided by your own avian vet. When in doubt always consult your own veterinarian.