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I suppose the first question would be, do you want the babies to survive? if the answer is yes then you're going to have to invest quite a lot of time and money into this venture. You would have to set up another tank, probably quite a big one, make sure it has adequate filtration. Keep the water in pristine condition at old times, a lot of tank maintenance in other words. You will also have to feed them on the correct food which in most cases is live baby brine shrimp. And then when they are big enough, you would have to find an outlet that would take them off your hands, unless you want to keep them all, depending on how many Oscars survive, you would have to get your self an absolutely huge tank, several hundred gallons.
My Oscars have laid eggs on occasions, but the ones I've got a moment haven't got as far as hatching out young. If it were to happen, I would just leave the fry to their own fate.It's not a straightforward task when breeding Oscars, it's certainly not something I would like to undertake because I just don't have the time or space any more.
You have to remember that we are dealing with fish that can reach in excess of 12 inches, if it was just guppies, then you wouldn't have to worry about tank size.