Agnieszka- I did a search as in the link below and there are lots of former posts on this topic. Does this area get any sun at all? If not you would be limited to things that like shade.

Here is a link that might be useful: shade under tree

If it were my tree I would have it taken down. It's too big for a developed neighborhood. I'll bet it's already dropping dead branches in several yards, including your own. Is it blocking views also?

hemnancy, I did a search but couldn't find anything that would apply to my situation... Thanks for the link; however, it talks about planting low growing things. I can come up with many of those, probably more than I have space for LOL. I'm having trouble deciding about something taller in there.
The area doesn't get any direct sun but it's quite bright.

botann, I can't remove the tree. It's on three properties and the other two neighbors would never agree to take it out. One of them is a great neighbor but the other one, the one I'm trying to screen from came to the fence screeming when I was cutting down an english laurel and removing ivy from another tree. All on my property but apparently, I was changing the view from her window. The ivy was hiding part of our house from their view. Doesn't matter that it was killing that other tree and hosting rats. Anyway, I digress!
Oh and the tree doesn't block any views. People here are more about preserving trees than removing them for views. Quite different from my former neighborhood ;)

Without the ivy may become an interesting feature as mosses and perhaps even ferns begin to clothe the trunk, if situation humid enough for these to occur on this specimen. Bigleaf maples are like the hotels of the woods here, hosting airborne growth like no other native broad-leaved tree.

A natural undergrowth for these is sword fern.

...might grow under there if the soil is sandy. Thing is the tree is the feature and another tree-like plant stuck under it will produce a conflict of scale. Better to furnish the space around the base of the tree and obscure part of the fence with rounded gloom-tolerant broad-leaved evegreen shrubs like aucuba, fatsia, skimmia and sarcococca (and of course ferns etc.). Small-leaved azara could also be espaliered onto the fence.

bboy, the ivy was on another tree in the garden... so I don't think there would be moss or ferns growing on the maple any time soon. Would be cool though..
Thanks for the plant suggestions. So you don't think that witch hazel would grow there? I see what you mean by conflict of scale but if I keep it in a shrub shape?

Already grows in a shrub shape on its own but is rather large-growing. There is a nice planting in the Seattlea arboretum of Chinese witch hazel with evergreen huckleberry beneath, in the Woodland Garden. The branches of the witch hazels spread over a bigger area than you have shown. Visiting the witch hazel family portion of the arboretum, if it is still intact and accessible (major changes of the south end of the park are in the works) might be a good idea, so you can see how big these often grow.

How about smaller, arching, clumping bamboo like Fargesia dracocephala. You'll have to water it but it would fit well in that spot.

Bboy, I'll check the arboretum to see some mature witch hazels. Can they be pruned into a smaller form?

Ian, I did think about a fargesia since I had one in my previous house and I liked it a lot. However, there's currently a row of bamboo to the right of that empty spot so I was hoping to plant something else there...

The vertical young canes in the center of the Fargesia would be apt to poke up into the branches of the maple visually, if not physically producing a tension. You want something low or at least spreading here, to align with and stay out of the branches of the maple. The azara also has an upright habit when untrained but if spread out on the fence would instead form curtains of small glittery evergreen leaves. Witch hazels can also be espaliered onto shady surfaces, see the planting at the north end of the Center for Urban Horticulture in Seattle for mature examples.

I will check the CUH witch hazel. Thanks!

The espaliered witch hazel at CUH is impressive. My pruning education (formal and practical) said to tread lightly with this plant family, so I was surprised by what I saw there. My winterhazel confirmed its dislike of pruning by sending up a bunch of water sprouts, tall straight growth through the middle of the plant, when I took off a couple of damaged stems. I imagine the gardeners at CUH are successful because the plants are very large, albeit 2-D, and the pruning has surely been done slowly and carefully. Keeping it in a shrub shape, if that means shortening most of the branches, may offer disappointing results.

You may want to consider disanthus a for a nice full shrub shape, although the fall color will be less spectacular in shade. Anything planted under a maple is going to be water-challenged, however. Maybe a native (oceanspray comes to mind) would do well.

Yes: If you lop back free-standing witchhazel family shrubs it doesn't turn out too well. With ones trained on a surface you are liable to be doing more tying in of branches and cutting off unwanted side shoots back all the way to the point of attachment to the main branch - except where the main branch has reached the edge of the surface. Using a large enough surface to contain the normal mature growth of the kind of plant used is an important part of getting an attractive effect, witchhazel family type or otherwise.

Well, I decided to get a witch hazel! I bought H. x intermediate 'Ruby Glow' today. It's already pretty big and it has a vase-like shape so I won't be able to espalier it which is OK. I'm hoping not to have to prune it at all... Thanks for all the suggestions! I'm going to consider espaliering some other plants once we change our sidings so I can let them grow undisturbed.

You better make a raised bed for a witch hazel and avoid it getting too dry. They don't look good drooping from lack of water.

Yes: Drought is not tolerated. These also get pretty big. Ans since you bought a dark one it will need something behind it to set it off, such as a white-variegated broad-leaved evergreen shrub. I also wonder how much it will be seen and enjoyed flowering during the winter back there, instead of near the house or front entrance.

Yes, I'm prepared to water it a lot. In fact, this area will be one of the first to get some kind of irrigation (drip or mini sprinklers, etc) because the bamboo planted next to it is quite thirsty.
I was thinking of planting a variegated kadsure vine on the fence behind the witch hazel for a nice contrast.
The backyard is not that big so I should still be able to enjoy the hazel in bloom even if it's not next to the house. And it's good if it gets me out of the house in the middle of winter!

If it shows up against the vine and you can look out a window at it then you will at least be able to see it that way. What really makes the dark ones show up is sun shining through them.

I hadn't heard of a kadsura vine before so I googled it and found it appealing. Doe's anyone that freezes in the low teens or below have any experience growing it?