If I want to do 10 gal batches how big should my MLT and HLT be?

If I wanted to do a 10gal batch do I actually need a 10+ gal HLT and MLT?

I am assuming that a 10gal cooler for the MLT would be sufficient to handle enough grain for a 10gal batch but I am not sure if you actually need 10 gal of hot water to mash the grain. My beer-sense tells me no.

I also assume that in an AG brew the brew pot should be larger than 10gal as you would add water to the malt generated from the mashing to get a little over 10gal to account for any evaporation during the boil.

For a 10gal setup are there "standard" or recommended sizes for the various tanks and tuns?

15 gallons minimum or 20 gal if you like. More is better because you can brew strong beers (big beers) if desired.

I also assume that in an AG brew the brew pot should be larger than 10gal as you would add water to the malt generated from the mashing to get a little over 10gal to account for any evaporation during the boil.

NO
the grain will soke up a bunch of water and after the spage you will have 11 to 12 gal or more of wort that will be boiled down to 10 over the one or more hour boil
when i do my 10 gal batches i put 15 gal in my HLT

You are definitely going to want more than 10 gal for the MLT if you want to brew a big beer (e.g. > 7% ABV).

You might be able to work with a 10 gal HTL because you can always add more water and heat it up accordingly as you go along, but it could be a big inconvenience.

You will probably want a keggle also.

I have a 10 gal HERMS setup and I can only do a single batch of big beer.

Like the first reply said, I would go with 15 gal all around just to be safe.