I'm not sure if you mean will delphiniums cross with hollyhocks, and the answer is no to that, or if your delphinium will cross with other delphinium and your hollyhock with other hollyhocks, and the answer to that is maybe.
If there are no there dephiniums or hollyhocks close by, the plants will self pollinate. If your neighbors are growing them, there's a chance of cross pollination. Whether they come true depends on the variety name of the plant and self pollination. Though a light blue delphinium if not true will probably produce babies in shades of blue. The hollyhock could make various colors or if it breeds true, they will all be red.
I sure hope that made sense.
Remy

Thanks Remy,

I have delphiniums (mostly blue to purple) and hollyhocks (pale pink to red) in close proximity. Will they tend to a common colour or maintain the range of colours, with some colours being more common?

You're welcome.
If grown in close proximity, the seeds will tend towards a dominant color from crossing. It is like the cosmos 'Sensation mix' with light pink, white, and medium pink. The seedlings in the first couple years will show some light pink or white, but mostly med. pink and in a few years they will all be med. pink, because that is the dominant color. I'm assuming for a delphinium it would be med. to dark blue and for the hollyhock a rosy pink.
Remy