Under a UCP LC, only the issuer or confirmer or nominated bank may "accept" drafts and the LC would signify the "drawn on" party that accepts them. Aval is not discussed in UCP and an applicant cannot "accept" drafts.
Under a collection, a company can aval however, this does not commit nor obligate any bank in the collection process to pay the draft at maturity.
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In addition, under a collection, a bank can (if so asked and they agree) add their guarantee to the payment of a term draft by way of an aval endorsement and the benefit of this guarantee of payment can be transferred through endorsement to other holders in due course.