Hot water line size

Uncertain about what size of hot water line to use.

Small structure: 1 shower, lav, toilet, washer, kit sink.

The cold water line is 3/4 pex reducing to 1/2 at the bibs, then to 3/8 at fixtures other than the washer. I will be using an on demand water heater connected to the pex through a length of iron pipe.

Question: Should I follow the same sizing for the hot water line as laid out for the cold water line or just run 1/2 pex for the hot throughout? The water heater has a 3/4 inlet and outlet.

follow the manufacturers directions. On demand heaters are sensitive to flow

Conventional wisdom says 3/4 copper ( 1" PEX) for the mains, reducing to 1/2" copper ( 3/4" PEX) for individual fixtures. These days, for low flow fixtures like lav faucets and showers, the smaller pipes have advantages. But for hi-demand fixtures like a tub or washing machine, you would quickly regret smaller pipes.

I'd get rid of that piece of iron/steel pipe and since all tank less water heaters are flow controlled (already), I'd not run less than 3/4" to it. Steel/iron pipe rusts adding iron to the water and hard water voids the warranty on the tank less heaters.