Sorry if this is really obvious. I bought some max statted pets to help me while I'm waiting for my pets to breed and train etc, but I noticed that all max statted pets are usually sold infertile. Does this mean that stats can be bred as well? If I train up some pets to max and breed them, will the offspring have max stats? Thank you very much and sorry if it's explained somewhere too. *stumbles about site*

Pets have stats- the things that grow as they're levelled, equipped, given proficiency- and they have Base Stats- which do not change once a pet reaches adolescence and can no longer be nurtured.

When you look at a pet's stats it's Stat: a (b +c)
In which a = 'active' stat, the one that alters with training
b = base stat, which is the inborn stat, and the point that the 'active' stat starts at
and
+c = grove stats, which are only present on pets obtained in the Lost Grove that have rarity above uncommon

'a' is what you increase when you train a pet, and 'b' is the stat that all the stats are... well... based on.
So you can't train a pet to be a max stat.

Base stats are inherited from parents, so if you have a pet with, say...
Pet 1:
Strength: 184 (22 + 0)
Intelligence: 772 (24 + 0)
Dexterity: 699 (25 + 0)
Agility: 272 (22 + 0)

is bred with
Pet 2:
Strength: 1,267 (80 + 0)
Intelligence: 239 (80 + 0)
Dexterity: 954 (79 + 0)
Agility: 327 (79 + 0)

Offspring's stats will be randomly:
Strength: between 22 and 80
Intelligence: between 24 and 80
Dexterity: between 25 and 79
Agility: between 22 and 79

and can be boosted with a philter at hatching, and nurturing while a hatchling.

So, yes, breeding two Max Stat pets would give you a max stat (both parents are 100 in their base stats, so there can't be any number swing), and this is why they're generally sold infertile (it takes a lot of time and effort and gold/diamonds to do a Max Stat project, so the breeders generally don't want people profiting off of their effort.
We've been working on our own Max Stat project for nearly a year now, and that was with pet stock that started with very much boosted stats. We're still probably two generations and several months from completion)

Brilliant! Thank you very much. I've got a long way to go :)