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If yes, then how rare is each one? Please don't question my curiosity.

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That didn't fully answer the question.
It didn't? I said that thay did  and gave you a link to the Rarity of them
Yes and I can't find a percentage Rarity but this should help a little bit and also if you have the National dex some things easier to find some things are unlocked that you couldn't get before
http://www.psypokes.com/dp/undergroundrarity.php

Accidentally put it as a comment I guess
Idk what sumwun means by this is isn't a complete answer, I clicked the link and I think it explained things, but maybe sumwun wanted a precentage
Yes, I wanted percentages. And information for Platinum.
But your link didn't have information for Platinum.
Well there are no percentages available sorry and I can't find any information on Platinum
That's exactly why this isn't a complete answer.
I'll run a test for you but it will take a while like Sunday
I think certain item's rarity depends on the trainer's ID# or secret ID#.But im not sure.
**Yes, each item found in the Sinnoh Underground have different rarities**. Some depend on your Trainer ID No. or whether or not you have obtained the Nat. Dex. Here's a List:

Spheres
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***Small Blue Sphere:*** Common
***Large Blue Sphere:*** Common
***Small Green Sphere***: Common
***Large Green Sphere:*** Common
***Small Pale Sphere:*** Uncommon
***Large Pale Sphere:*** Uncommon
***Small Prism Sphere:*** Uncommon
***Large Prism Sphere:*** Uncommon
***Small Red Sphere:*** Common
***Large Red Sphere:*** Common

Fossils
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***Armor Fossil:*** Uncommon, if trainer ID is even in number.
***Claw Fossil:*** Rare (After Nat. Dex), Found rotated by 90, 180 or 270 degrees.
***Dome Fossil:*** Rare (After Nat. Dex).
***Helix Fossil:*** Rare (After Nat. Dex), Found rotated by 90, 180 or 270 degrees.
***Old Amber:*** Rare (After Nat. Dex), Found rotated by 90 degrees.
***Root Fossil:*** Rare (After Nat. Dex), Found rotated by 90, 180 or 270 degrees.
***Skull Fossil:*** Uncommon, if trainer ID is odd in number.

Plates
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***Draco Plate:*** Very Rare
***Dread Plate:*** Very Rare
***Earth Plate:*** Very Rare
***Fist Plate:*** Very Rare
***Flame Plate:*** Very Rare
***Icicle Plate:*** Very Rare
***Insect Plate:*** Very Rare
***Iron Plate:*** Very Rare
***Meadow Plate:*** Very Rare
***Mind Plate:*** Very Rare
***Sky Plate:*** Very Rare
***Splash Plate:*** Very Rare
***Spooky Plate:*** Very Rare
***Stone Plate:*** Very Rare
***Toxic Plate:*** Very Rare
***Zap Plate:*** Very Rare

Additional Items
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***Blue Shard:*** Uncommon
***Damp Rock:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex).
***Everstone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex).
***Fire Stone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex).
***Green Shard:*** Uncommon
***Hard Stone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex).
***Heart Scale:*** Uncommon
***Heat Rock:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex).
***Icy Rock:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex).
***Iron Ball:*** Very Rare
***Leaf Stone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex), Found Rotated by 90 degrees.
***Light Clay:*** Very Rare
***Max Revive:*** Very Rare
***Moon Stone:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex), Found Rotated by 90 degrees.
***Odd KeyStone:*** Very Rare
***Oval Stone:*** Rare
***Rare Bone:*** Very Rare, Found rotated by 90 degrees.
***Red Shard:*** Uncommon
***Revive:*** Very Rare
***Smooth Rock:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex).
***Sun Stone:*** Very Rare (Pre Nat. Dex), Rare (After Nat. Dex).
***Thunder Stone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex).
***Water Stone:*** Very Rare (Pre Nat. Dex), Uncommon (After Nat. Dex).
***Yellow Shard:*** Uncommon

> Sources: Serebii, PsyPokes, Experience.
Just a suggestion, maybe include that you wanted exact percentages and specific information regarding Pokemon Platinum in with the question description. Would have saved me some time knowing that I didn't even have to type out that entire list in the first place :P
What do "common", "uncommon", "rare", and "very rare" mean?
Unfortunately, I am unaware of that. In your question and description, you simply asked if these items had rarities, not the percentages or exact definitions of what they meant. Through the sources I have looked through in combination with my personal experience in Sinnoh, these rarities do seem accurate by wording and general meaning. My apologies if I didn't provide satisfactory information.
If you don't know what "common" and "rare" mean, then I don't know either. Answering, "how rare are they?" by saying "rare" is like answering, "what time is it?" by saying "late". It's not my fault you spent about 15 minutes typing an answer that contains no information.
I also asked, "how rare is each one?" And you said something like, "uncommon" or "rare" for each one. That's like answering, "what time is it?" by saying "late".
Can you do me a favor by either hiding this answer or converting it into a comment? That way this question goes back to the unanswered list and someone who knows the answer might find it.
Will do!
Thanks, I guess.

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Best answer

I wont question your curiosity but you are quite picky but I finally looged back in many sundays and a thursday later found this in my updates and decided to answer it.(I actually answered it a while ago I just forgot to take this from the other document and paste it here). So here it is:
First of all to clarify the ID# number thing is a myth. doesn't exist wouldn't be fair if everyone didn't have equal chances. and I'll spare you the values (more like me since I have to handcopy because it is illegal to copy straight out of the sourcecode).but heres the percentages hope this is what your looking for....

Common:58.7%
Uncommon:25.3%
Rare:10.7%
Very Rare:5.3%

the values shouldn't matter to much anyway wouldn't changes the percents that's what your after right? So I hoped this helped if this isn't what you want if you want themvalues and the decimals on the percentages well I don't know what to tell you this was pre written and that copy of the game is in the proccess of being rewritten to my liking. so I can't find those anyways. But I hoped this helped!

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Did you really ROM hack to answer this question?
Sometimes you have to hack to answer to certain questions
No I looked at the source code and decrypted it (they used a variation of python back then). But  I'm ROM hacking right know so I can rewrite Pearl To Goat and all that good stuff.No it's probaly one of the easiest ones I've done I remember Rom hacking  Moon to find out Poke pelago bean rarities and percentages because It was to cryptic for me to do it any other way luckily I've learned how to fix ROM hacking so I can know do it and it won't be permanent so I'm not to worried about it,