It varies and depends on the year of car, type of car, dealer etc. Some main dealer brands have "approved" used cars that come with a 2 year warranty. Most independent dealers will give 3 months or maybe 6 that only covers engine and gearbox
You need to ask who is providing the warranty. If you're being offered three month warranties then I suspect you're talking to independent dealers and their warranties are typically based on goodwill i.e. the dealer has to foot the bill if there's a fault that needs fixing. In that case, the warranty may not be worth the paper it's written on. That's if they even bother to hand you a piece of paper telling you what is and is not covered.
Some dealers at the last minute hand the customer a receipt which says 'sold as seen' which (illegally) implies that there is no warranty at all.
Whatever you do, do not buy on the basis that some fault you're aware of (e.g. fault light on the dashboard, strange noise from the engine) will be fixed afterwards by the dealer under his 'warranty'. The same applies to an expired NCT. Get the car thoroughly checked out and only buy on the basis that you will not be darkening his door for a long time.