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Is there overhead kb in every transaction?
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There is overhead, but it is bytes, not kilobytes. (of course if you create enough transactions those bytes will add up to kilobytes eventually).
Every
transaction has
10 bytes of overhead.
Every
output will require another
34 bytes. Since you are consolidating, I assume each transaction will have only 1 output?
Combined, that's
44 bytes per transaction.
Then every
input will require between
147 and 149 bytes.
You may find that it is cheaper to just use the inputs in transactions without consolidating them. You are going to have to pay for that overhead when you spend the bitcoins. Why pay it twice? (Once when you consolidate, and again when you spend.) It will only be beneficial if you can pay a significantly lower fee per byte during consolidation, so that you'll have less bytes to pay for later when the fee per byte is higher.