Residential hot water loop pipe sizing

I am installing a dedicated hot water loop in a 5 story rowhouse (think tall, narrow, but deep) in NJ. The HW tank is at the lowest level and water will be delivered to fixtures on all levels. My question is whether the reurn line from the dedicated loop should be the same diameter as the supply line. I assume so, but if not, what is the intuition (or theory) on why it should be smaller (or larger!).

The size of the return line depends on the flow rate of the pump used.

I’m guessing you are not a plumber.

Did you pull a permit?

haha. Indeed I am not a plumber. My plumber did pull permits so we are legit. I am just questioning the size of the return line since it’s not specified on the plans and my current house has the return the same size as the supply. I am worried that the loop won’t function properly with smaller size return. But I think you are saying it will, so long as the flow rate on the pump is somehow matched to the length of the run and the pipe size.

My current pump is on a timer which works great. We circulate the water in the loop from 5am-10pm. All faucets except the kitchen have hot water within 3-4 secs while the kitchen takes more that 4 times as long. I presume that the kitchen is taking longer because it’s distance from the loop is 4 times as long as the other fixtures.

Is there a rule of thumb for length of time it should take?