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I understand that in order to maintain an account in state on the Relay Chain an account needs to hold more than the Existential Deposit (1 DOT/0.000003 KSM), but I am wondering if assets deployed on Statemint/Statmine also need to maintain a minimum balance to avoid being reaped. If so how is this determined?

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Assets (from assets pallet) do not have existential deposits but the native token (pallet balances - ED) does. For example, if you want to create a new asset in Statemine and since the native token of Statemine is KSM then you need to have in your Statemine account an existential deposit of 0.000003 KSM.

However, what the asset pallet has is the notion of Sufficiency and the attribute is_sufficient

So if an asset is deemed as sufficient (through governance) then the existential deposit is not needed.

As mentioned in the wiki :

Only the network's governance mechanism can deem an asset as sufficient. A balance of a non-sufficient asset (the default) can only exist on already-existing accounts. That is, a user could not create a new account on-chain by transferring an insufficient asset to it; the account must already exist by having more than the existential deposit in DOT (or a sufficient asset). However, assets deemed sufficient can instantiate accounts. In the future, sufficient assets will be able to pay transaction fees, such that users can transact on Statemint without the need for DOT .

An example proposal of this case is from RMRK where the notion of Sufficiency is again explained

Sufficiency is the concept of allowing a token on Statemine to exist and be used without accounts needing an existential deposit of KSM to accept the token.

and in which they proposed to make the RMRK token sufficient so no need for existential deposit in KSM.

Adding additional resources that give more context on the above :

To hold a non-sufficient asset in an account, the account needs to exist on-chain, which means it needs to have a balance in the native asset at least as much as the Existential Deposit (ED). This means 0.1 DOT on Statemint and 0.000003333 KSM on Statemine. As you may have noticed, these existential deposits are ten times smaller than they are on the Relay Chains. So, to send a non-sufficient asset, you need to ensure that the recipient account has at least the ED. A sufficient asset doesn't require the account to have any balance in the native token in order to be received.

The sufficients reference counter indicates if an account is self-sufficient and can exist by itself. For example, in the Assets pallet, an account can have sufficient number of certain assets but without owning any native account balance.

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The Existential Deposit (ED), transfer fees, and the deposits for proxy/multisig operations on Statemint are about 1/10th of the values on the Relay chain. So, the Existential Deposit of a Statemint account is 0.100 DOT, when compared to 1 DOT on Polkadot.

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