How a "capitalization" is translated on the Balance Sheet, Income Statement, and Statement of Cash Flows

Hi everyone,
So this is a question for my understanding of the bigger picture of a company’s financial statements.
Here is what i think:
At Balance Sheet level: I know that when we chose to capitalize an item instead of expensing it, we debit the asset’s Balance sheet item, and credit cash. So this just has 0 impact overall on the BS at the year of capitalization (+value of the asset in the asset’s account -value of the asset in the cash account).
At Income Statement level: We don’t report anything. I guess this is correct given what i just stated for the BS part (no impact).
At Statement of Cashflows level: I think we record -value of the asset, in the Cash flow from investing section.

Am i correct about all of the above?

After the year of capitalization, we start depreciating the asset, and it translates in reporting yearly expenses in the IS. In terms of BS entries, we credit Accumulated depreciations account and debit Depreciation expense. And i think that’s it, no Cashflow entries.

Am i correct?

Thanks in advance guys.

Assuming that you paid cash (as opposed to financing the purchase with a loan), yes.

Yes.

Note that depending on the nature of the asset, you might depreciate it, amortize it, deplete it, or accrete it, with corresponding changes to the expense and accumulated account names. Functionally, they’re all the same.