To potty train a three year old boy you should just remove the diapers and pull ups and allow him to pee and poop himself in underwear.
In diapers and pull ups he cannot feel the pee as it's absorbed and the diaper can make the poop not feel as bad either.
But when poop is in underwear or pee is in underwear it feels more gross and he will likely decide eventually to use the toilet.
You should go cold turkey on the diapers and just stick him in underwear and keep reminding him to use the toilet and take him there yourself.
However some kids are not fully ready at 3 years old and may not potty train fully until 4 years old which is okay.
Diapers come in size 7 and even 8 in some brands including Pampers and Huggies diapers which should easily fit your 3 year old boy and even up to a 10 year old boy.
Potty training can take days and even weeks or even some months for some children to get fully potty trained and it's normal for them to have accidents and pee and poop their pants but if you stick with it he will eventually stop wearing diapers and use the toilet.
Signs of readiness for potty training include.
Keeping Diaper Dry longer than 3 hours or having fewer wet diapers per day.
Child holds his or her pee in and then pees at once.
Child hates wearing diapers or asks for a diaper change.
Pulling at a wet or dirty diaper.
Hiding to pee or poop.
Showing Interest in others' use of the potty, or copying their behavior.
Having a dry diaper for a longer-than-usual time.
You're changing fewer wet diapers.
Your child's bowel movements are predictable.
He broadcasts bodily functions.
He or She despises dirty diapers.
He's able to perform simple undressing.
He understands bathroom lingo.
It is very normal for a 3 year old to not be potty trained.
While some kids are potty trained before their 3rd birthday it's perfectly normal and fine for a 3 year old and even a 4 year old to wear diapers and not be potty trained.
Some kids will potty train around 3 years and 6 months of age and some not until age 4 and in some rare cases a child may not potty train until age 5 or close to age 5.
Most kids potty train and stop wearing diapers between the ages of 18 months to 2 years old.
However every kid is different and it's normal for even a 3 year old and 4 year old to not be potty trained.
Eventually a kid will potty train even if you don't try to potty train them yourself.
The oldest age for potty training is 5 years old.
I have a 5 year old son who is not fully potty trained but I'm sure he will be potty trained soon.
He wears diapers full time because he does not always get to the toilet so I keep my 5 year old in diapers full time until he goes to the toilet every time.
If he does not get potty trained by age 6 then I'm gonna force the issue but for now I'm letting him decide.
Most kids are potty trained before age 4 years old and some kids potty train as early as age 18 months to 2 years old.