In general, yeah you can choose any arbitrary address that you want for null address.

The reason you can do that is because it is almost impossible for you to choose a random address that somebody already has a private key for it. Let's do some math to prove it, an address is 256 which mean it can go up to 2^256. The earth population at this time (12/2021) is about 7.9 billion but i will make it 8 billion for ease in calculation. Assume every person in the planet has 100 private key corresponding to the address they have. Then the possiblity that you can choose an address that they already choosen is about 10^-66 (https://www.wolframalpha.com/input/?i=800%2C000%2C000%2C000+%2F+2%5E256).

The possiblity that you win a Powerball is one in 292.2 million, roughly 10^-9 (https://www.thebalance.com/what-are-the-odds-of-winning-the-lottery-3306232). So you will have to win Powerball roughly 7 times in a row to even get a chance in picking a random address that somebody already has the private key given that everybody on the earth have 100 private keys

Answer from KishouYusa on Stack Exchange
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Etherscan
etherscan.io › address › 0x0000000000000000000000000000000000000000
Null: 0x000...000 | Address: 0x00000000...000000000 | Etherscan
Get 177% Deposit Bonus and 25 Jackpot Spins. Fast crypto withdrawals. ... This address is not owned by any user, is often associated with token burn & mint/genesis events and used as a generic null address
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Etherscan
etherscan.io › address › 0x000000000000000000000000000000000000dead
Null: 0x00...dEaD | Address: 0x00000000...00000dead | Etherscan
Play original casino games and VR slots. Get 177% Deposit Bonus and 25 Jackpot Spins. Fast crypto withdrawals. ... This address is commonly used by projects to burn tokens (reducing total supply).
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Etherscan
etherscan.io › address › 0x0000000000000000000000000000000000000001
Null: 0x000...001 | Address: 0x00000000...000000001 | Etherscan
Null: 0x000...001 · Blocked · Burn · API · Token Approvals Beta · Validate Account Balance Check Previous Balance · Update Name Tag or Label · Remove Name Tag · Report/Flag Address · 56.886827096841336665 ETH · $173,872.53 (@ $3,056.46/ETH) >$14,292,335.37 (>401 Tokens) Could not find any matches!
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Reddit
reddit.com › r/ethereum › null address holds newly minted tokens?
r/ethereum on Reddit: Null address holds newly minted tokens?
December 30, 2021 -

Hey! I am trying find out who is holding the game specific nfts on etherscan. While searching, I saw null address that holds nfts. Then, I searched online and it happens to be that somebody accidentally sent to wrong address. However, when I looked at the inventory of null address, I saw these are newly minted nfts and there is no other transaction. On the transactions it says nft is transferred to some other addresses however I can't find the tokens on those addresses as well. I feel lost now, any explanation is highly appreciated. Thanks in advance!

Inventory of null address

Example transaction

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Etherscan
etherscan.io › address › 0xdead000000000000000042069420694206942069
Null: 0xdea...069 | Address: 0xdead0000...206942069 | Etherscan
To use this feature, please login to your Etherscan account and return to this page. ... A private note (up to 500 characters) can be attached to this address. Please DO NOT store any passwords or private keys here.
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Etherscan
etherscan.io › address › 0x1111111111111111111111111111111111111111
Null: 0x111...111 | Address: 0x11111111...111111111 | Etherscan
To use this feature, please login to your Etherscan account and return to this page. ... A private note (up to 500 characters) can be attached to this address. Please DO NOT store any passwords or private keys here.
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Etherscan
etherscan.io › address › 0xeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Null: 0xeee...eee | Address: 0xeeeeeeee...eeeeeeeee | Etherscan
To use this feature, please login to your Etherscan account and return to this page. ... A private note (up to 500 characters) can be attached to this address. Please DO NOT store any passwords or private keys here.
Find elsewhere
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Etherscan
etherscan.io › address › 0x0000000000000000000000000000000000000003
Null: 0x000...003 (0x0000000000000000000000000000000000000003) | Address 0x0000000000000000000000000000000000000003 | Etherscan
The Address 0x0000000000000000000000000000000000000003 page allows users to view transactions, balances, token holdings and transfers of ERC-20, ERC-721 and ERC-1155 (NFT) tokens, and analytics.
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Etherscan
etherscan.io › address › 0x0000000000000000000000000000000000000008
Null: 0x000...008 (0x0000000000000000000000000000000000000008) | Address 0x0000000000000000000000000000000000000008 | Etherscan
The Address 0x0000000000000000000000000000000000000008 page allows users to view transactions, balances, token holdings and transfers of ERC-20, ERC-721 and ERC-1155 (NFT) tokens, and analytics.
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Etherscan
etherscan.io › address › 0x0000000000000000000000000000000000000004
Null: 0x000...004 | Address: 0x00000000...000000004 | Etherscan
To use this feature, please login to your Etherscan account and return to this page. ... A private note (up to 500 characters) can be attached to this address. Please DO NOT store any passwords or private keys here.
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Arbitrum One
arbiscan.io › address › 0x0000000000000000000000000000000000000000
Null: 0x000…000 | Address: 0x00000000...000000000 | Arbitrum One
This address is commonly used by projects to burn tokens (reducing total supply) or mint tokens (increasing total supply).
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Etherscan
optimistic.etherscan.io › address › 0x000000000000000000000000000000000000dead
Null: 0x00...dEaD | Address: 0x00000000...00000dead | OP Mainnet Etherscan
This address is commonly used by projects to burn tokens (reducing total supply). Null: 0x00...dEaD · Burn · API · Token Approvals Beta Check Previous Balance · Update Name Tag or Label · Remove Name Tag · Report/Flag Address · ...
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Reddit
reddit.com › r/etherscan › null address balance
r/etherscan on Reddit: Null Address balance
July 13, 2022 -

I'm trying to find out the amount of tokens that have been burned (sent to the Null Address) for a particular token on PolygonScan. However, the balance is 0: https://polygonscan.com/token/0x2721d859ee8d03599f628522d30f14d516502944?a=0x0000000000000000000000000000000000000000

Is it because tokens minted by the Null Address effectively count against the burned ones (reduce the balance)? If so, how can I find out how many tokens were burned?

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Etherscan
goto.etherscan.com › address › 0x0000000000000000000000000000000000000000
Address: 0x00000000...000000000 | Etherscan
... 100s of games, generous bonuses, 20+ years of trusted gaming. Join CryptoWins & start winning today! This address is not owned by any user, is often associated with token burn & mint/genesis events and used as a generic null address
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Etherscan
etherscan.io › address › 0x0000000000000000000000000000000000000005
Null: 0x000...005 | Address: 0x00000000...000000005 | Etherscan
To use this feature, please login to your Etherscan account and return to this page. ... A private note (up to 500 characters) can be attached to this address. Please DO NOT store any passwords or private keys here.
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Etherscan
etherscan.io › address › 0xff00000000000000000000000000000000081457
Null: 0xFf0...457 (0xff00000000000000000000000000000000081457) | Address 0xff00000000000000000000000000000000081457 | Etherscan
Claim Now! 100s of games, generous bonuses, 20+ years of trusted gaming. Join CryptoWins & start winning today! This address is used by Blast as their Batch Address. Null: 0xFf0...457 ·
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Etherscan
etherscan.io › address › 0x0000000000000000000000000000000000000002
Null: 0x000...002 (0x0000000000000000000000000000000000000002) | Address 0x0000000000000000000000000000000000000002 | Etherscan
The Address 0x0000000000000000000000000000000000000002 page allows users to view transactions, balances, token holdings and transfers of ERC-20, ERC-721 and ERC-1155 (NFT) tokens, and analytics.