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A little riddle I conceived on vacation last winter.

I am spread out like a leaf.
That what forms me cuts me, but builds me up.
That what cuts me seeks always to go lower, but lifts its bed higher.
I am commonly found where what builds me is less common.
What am I?

Hint: see title

In answer to ermanen, I've decided to post one more clue: leaf

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It could be an

Alluvial fan

I am spread out like a leaf.

It's spread out, and may appear to have "veins" much like a leaf. The leaf in the hint looks like a fan as well.

That what forms me cuts me, but builds me up.

Streams erode rock, but carry the sediment/alluvium required to build up the alluvial fan

That what cuts me seeks always to go lower, but lifts its bed higher.

Streams flow downhill because of gravity, but in doing so pick up the sediment which will build up the alluvial fan

I am commonly found where what builds me is less common.

Water builds alluvial fans (most of the time), but they're often found in arid climates / desert regions

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  • $\begingroup$ We have a winner! $\endgroup$ – Joshua Feb 12 '16 at 17:09
  • $\begingroup$ Incidentally, this answer was posted late at night on Feb 7 and deleted a few minutes later, only to be undeleted yesterday. I saw it today on the bottom of the list. $\endgroup$ – Joshua Feb 12 '16 at 17:12
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Second attempt (first attempt below):

River delta

Line 1:
I am spread out like a leaf.

The water parts of a delta look similar to the veins of a leaf.

Line 2:
That what forms me cuts me, but builds me up.

Water erodes a delta, but also builds it up by depositing silt.

Line 3:
That what cuts me seeks always to go lower, but lifts its bed higher.

Water always flows downhill, but the "bed" of a river or river delta is built up by the sediment it carries.

Line 4:
I am commonly found where what builds me is less common.

The river delta is formed by fresh water, but the delta is at the ocean, where salt water reigns.

First attempt:

River OR riverbed

Line 1:
I am spread out like a leaf.

A leaf has "veins" that transport liquid, just like tributaries and smaller streams lead into the main river. If you looked at a system of rivers/riverbeds, it would look like leaf veins.

Line 2:
That what forms me cuts me, but builds me up.

Water forms a riverbed and "cuts" it through erosion, but also builds it up by depositing dirt, rocks, etc.

Line 3:
That what cuts me seeks always to go lower, but lifts its bed higher.

Water always flows downhill, but again the "bed" of the river is built up by the sediment it carries.

Line 4:
I am commonly found where what builds me is less common.

Not as sure about this one. If the answer is "riverbed" then those are often found where the water in the river has run out. Otherwise, it might be referring to the fact that rivers more often show up when there aren't lakes around (I'm not even sure if that is true). Still thinking on this line.

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  • $\begingroup$ No, that's not it. Nice try though. Press on and you might figure it out. $\endgroup$ – Joshua Feb 5 '16 at 23:12
  • $\begingroup$ Specifically, a distributary delta. A delta is commonly found impinging into a sea, where fresh water is less common. $\endgroup$ – Jasper Feb 5 '16 at 23:42
  • $\begingroup$ Now Jasper is close. $\endgroup$ – Joshua Feb 5 '16 at 23:48
  • $\begingroup$ That's actually just the edit I was working on. Joshua's comment seems to indicate it's not quite right. $\endgroup$ – Duncan Feb 5 '16 at 23:49
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What am I?

History

I am spread out like a leaf.

Referring the the leaves/pages of the books written to cover the histories of different era

That what forms me cuts me, but builds me up.

History consists of facts which are remodelled (cut and built) as per the current generation of rulers and historians.

That what cuts me seeks always to go lower, but lifts its bed higher.

Anyone who wishes to have his name marked in history tries to aggrandize him/herself and in the process belittle(lower) the other one. Say, Mughals invading Inda: could be aggrandized by the Mughal historians but belittled by the Indian rulers.

I am commonly found where what builds me is less common.

History most times is about places or people who are no longer living (what builds me is less common i.e does not exist).

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What am I?

Canyon

I am spread out like a leaf.

Canyons spread out like a leaf where the branches of the river that form the canyon look like the veins that carry the water.

That what forms me cuts me, but builds me up.

River forms the canyon and it cuts through the ground.

That what cuts me seeks always to go lower, but lifts its bed higher.

Because of downcutting, the canyon gets deeper and the stream bed stays higher.

I am commonly found where what builds me is less common.

Canyons are more common in arid than in wet areas.

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  • $\begingroup$ I'm impressed that somebody found another close match. Built up is supposed to be literal, not cutting away the surroundings less. $\endgroup$ – Joshua Feb 10 '16 at 19:23
  • $\begingroup$ @Joshua: I thought you have visited the Grand Canyon :) I'm confused now, how close I am? :) Is it an estuary or a delta plateau maybe? $\endgroup$ – ermanen Feb 10 '16 at 19:31
  • $\begingroup$ No and no; and you find neither in the desert as I already indicated in a comment to Kola. $\endgroup$ – Joshua Feb 10 '16 at 21:04
  • $\begingroup$ @Joshua: I thought you eliminated the word "delta" already but the answers seems to be "Nile Delta" now. $\endgroup$ – ermanen Feb 10 '16 at 22:01
  • $\begingroup$ Try scaling back the amount of water some more. $\endgroup$ – Joshua Feb 10 '16 at 22:28
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Is it

Sand

It's spread out like a leaf.

That what forms me cuts me, but builds me up :

river/sea

That what cuts me seeks always to go lower, but lifts its bed higher :

river/sea cuts sand and goes low by each layer of sand bed it makes.

I am commonly found where what builds me is less common :

desert

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  • $\begingroup$ You got every clue wrong but the last one :( $\endgroup$ – Joshua Feb 10 '16 at 0:26
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Looks to me like

A book

Spread out like a leaf

These would be the leaves (pages) of the book

Cuts me up but builds me up

The press trims the leaves and binds them together

Seeks to go lower but lifts its bed higher

The bed of the press during the printing and binding process

Found where what builds me is less common

Few printing presses in forests.

Ta-da!

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  • $\begingroup$ Oh, I like this answer $\endgroup$ – question_asker Feb 12 '16 at 15:04
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I'll Guess

Fossil

I am spread out like a leaf.

Just a fossil formed from a plant

That what forms me cuts me, but builds me up.

Water Erodes the Shape into the rock

That what cuts me seeks always to go lower, but lifts its bed higher.

The Water Builds up over time

I am commonly found where what builds me is less common.

Fossils often found in deserts where water is less common

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  • $\begingroup$ Unbelievable. A completely wrong answer that matches all the clues. $\endgroup$ – Joshua Feb 12 '16 at 17:09

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