I think a lot could be learned from the way very tall trees make it work here on earth.
Scientists are making some pretty interesting discoveries about how the redwoods are reaching their impressive heights. It appears that the redwoods are collecting water from the top and the bottom by drinking water from the ground as well as from the canopy.
Some redwoods have lived since the days of Jesus Christ. With time,
their immense, complex canopies trap needles, dust and seeds, creating
peaty soil mats a yard thick and as big as a bus that grow plants,
sustain animals and absorb water hundreds of feet above the ground.
"Eventually, you get this huge sponge that builds up," said Steve
Sillett, a Humboldt State professor who began studying the phenomena
in redwoods in 1996. "During most of the year, it's an aquatic
environment up there" fed by rain and fog.
He's discovered mollusks, crustaceans and other animals ordinarily
found in stream beds -- even the wandering salamander, which lacks
lungs and must stay moist to absorb oxygen through its skin.
Like trees in the Pacific Northwest and other temperate rain forests
and cloud forests, the redwoods sprout canopy roots from their
branches that Sillett believes take in water and nutrients from the
Effectively the trees create their own little gardens high up in the canopy and sprout canopy roots or adventitious roots to collect water and nutrients.
Another path or even a combined approach might be the use of aerial roots:
Aerial roots: roots entirely above the ground, such as in ivy (Hedera)
or in epiphytic orchids. Many aerial roots, are used to receive water
and nutrient intake directly from the air - from fogs, dew or humidity
in the air.
Scaling this up to kilometers may be a bit of a stretch, but it does solve the water issue.
Just had a thought on a way to potentially work around the kilometer issue...
What if your trees were partially petrified? As in the inner core of the trees turned to stone by absorbing minerals from the soil. You may think this would mean that your trees would have to be millions of years old, but that may not necessarily be the case:
The rate of petrifaction is not exactly known. In some cases it may be
fairly rapid. For example, mine timbers have been partly petrified
after a few years' exposure to mineral-laden water. Most petrified
wood was formed long ago. For instance, stone logs in Petrified Forest
National Park, Arizona, are of the Triassic Period and more than
160,000,000 years old.
Again this is probably stretching a little far, but it may give your trees the added strength they need to grow to the heights your looking for.
Another option may be to have your trees form an interconnected network, like The Great Banyan
having branches roots and trunks interconnected may offer some really significant strength advantages.
"Acharya Jagadish Chandra Bose Indian Botanic Garden - Howrah 2011-01-08 9724" by Biswarup Ganguly - Own work. Licensed under CC BY 3.0 via Wikimedia Commons.