This is a loaded question with a loaded answer! But first let me make a few points clear.
1. Yes they grow to the size of their parents, all mammals do and we have very similar DNA to pigs
2. No teacups, nanos, pixies, pocket pigs and micro pigs DO NOT exist!
3. Pigs grow for 3-5 years
Mini pigs are decedents of Pot Bellied pigs imported in the 1980's. They do not have to be 300 pounds! Find a breeder who breeds the smaller lines 14-16" and have many generations to show you. We have up to 8 generations in some of our lines. No pig over 16" is bred! We shoot for 13-15" but health and dispositions play a role and we have to pick the best overall pets that will make wonderful, healthy family pets. Our Pigs are called American Miniature Pigs. They have been bred down since the 80's into small (below my knees, I'm 5'1") loveable pets that can be kept indoor/outdoor and don't get 300 pounds unless grossly obese.
No piglet is ever going to be 10" or under 40 pounds as an adult unless grossly underfed, like an anorexic person. I have listed examples below, we do 400-500 visitors a year and I was a co-founder of the National Non Profit to help educate people.
Most importantly remember these terms are not breeds: Teacup Pig, Micro Pig, Nano Pigs, Pixie Pigs.... they are all various sizes of Miniature pigs, these terms are used mostly by people charging alot and trying to convince you that tiny pigs stay tiny...essentially scams! Schedule a visit if you are unsure if a pig is right for you. Better to spend $50 on an hour visiting adorable animals than $2500 on a scam that you will be unhappy with