If I understand correctly - Subledger Accounting Method (SLAM) is assigned to ledger and that SLAM is defined in SLA to which applications (payables, assets etc) are assigned and other configurations such as AAD, Journal Definitons etc are configured for each AAD.

My Question: If we define custom AP application just to separate the custom objects from standard AP directory structure - How does SLA account the transactions from a custom AP responsibility which is tied custom AP application? In other words - will SLA pick up the transactions entered via custom AP application...if yes how does SLA know this? where is the link between custom AP and standard AP applications?

SLA module is tightly integrated with Oracle E-Business Suite modules. Modules like AP and AR generate business events. In turn SLA module generates accounting based on predefined rules.
Oracle offers a similar product called Financial Services Accounting Hub which could be used with any custom application including non-Oracle applications. I hope this helps.

My question was related to custom application definition in place of standard application like AP. I actually figured out that there is a patch available for R12.1 that delivers profile option called "SLA : Alternate Application Id" where we need to link the standard application like Payables to a custom payables application at application level. After applying the patch - we can now run create accounting from custom AP application which was erroring out before.