Rhododendrons have a shallow rooting habit, with a dense network of fine surface roots that will extend out as far as the widest branches. You will find a few larger anchoring roots, but for the most part taking one out completely including the rootball is a reasonable job.

A healthy established rhododendron will resprout if cut down low - if you wish to replant a tree in the same site you'll want to remove the roots. Just a tip - when cutting it back as part of the taking out process, leave some stem height for handholds, it will make removing the rootball easier.

Rhododendrons grow best in soil that is acidic, but they don't contribute to the soil acidity or make it more acid - there is nothing for the soil to recover from. You'll need to know what type soil you have when choosing an appropriate tree for your area; a local nursery can help you with that choice.

If the rhododendron was healthy & green, then the native soil must be acidic, and therefore a blueberry shrub might thrive in that location. Blueberry shrubs can do well in relatively thin soil, they like full sun. They will not survive an extended drought, unless they are watered every week or so. The lowbush and dwarf varieties are tougher, and require less care. They also produce less fruit. Highbush blueberry shrubs can yield 2 to 8 kilograms of fruit per year, when they are full grown, at about 5 years.

Dear Morz8 and ericwi,

thank you very much to both of you for your very useful replies, you have answered my questions perfectly.
Good tip about leaving a handhold, thanks, I'll do that.
The leafy branches have been removed, but we still need to tackle the stems and rootball.

I thought that the tree's fallen leaves would have affected the soil's pH over the years, and of course it now makes sense that the soil would have been acidic in the first place, as the tree was doing well. Only other things growing in the garden at the moment are some conifer-type trees.

With the tree's branches removed, I now have considerably more light in my room overlooking the site, and am starting to doubt whether I still want to plant a fruit tree there, which will create shade again. Although it seems that apples do like acidic soil, and it looks like one can get some nice 'heirloom' types here.

I like the idea of the blueberries, and didn't realize that they like acidic soil (I'm new to northern hemisphere gardening, which is probably obvious). I suspect that all the soil is probably on the acidic side here, as there are rhododendrons everywhere. (also blueberries in the foresty bits, but the small bushes with single, not clustered berries - bilberries?).
I read that you need 2 or 3 different types of blueberries for them to bear fruit. I'll have to go and have a chat with the local nursery. There's a lot to learn. I'm very keen on all types of edible plants, particularly indigenous ones, but very unsure of what survives in this climate (there are a lot of climate zones here, need to do some homework)
oh yes, no chance of drought here - apparently Bergen has one of the highest rainfalls in the world!

thanks again for your kind advice, I am relieved to know that removing the root ball shouldn't be too much of a problem, and that the soil is not 'damaged' in any way.