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On April 17 the EFSF made a 25 bb loan to the Hellenic Financial Stability Fund (HFSF) guaranteed by the Greek government. The HFSF used these funds from the EFSF to buy 25 bb EUR of 6-10 yr EFSF FRN MTN bonds.

On May 28th, 18 bb of the 25 bb EFSF bonds were sold to the Greek banks by the HFSF in return for convertible bonds or new shares in the bank.

The EFSF bonds are eligible collateral at the ECB and are thought to have been used to replace previous ELA borrowings by the same Greek banks.

This operation gives the Greek banks capital plus improved funding with the Greek government ultimately liable for the initial loan from the EFSF. However, no EFSF bonds were needed to be issued to the market. Effectively the ECB financed the Greek banking systems recapitalization.

The total amount set aside by the EFSF for Greek bank recapitalizations is 48 bb euro.

A similar structure could likely be done in Spain:

ESM makes a loan to the FROB (loan gtd by Spanish govt) to buy ESM bonds
The FROB buys ESM bonds
The FROB then sells the ESM bonds to banks in return for convertible bonds or common stock ownership in the bank
The Spanish bank then has a capital injection and the ability to post ESM bonds at ECB for funding

This avoids in theory at least, the ECB directly bailing out the Spanish banking system