The singer's filing Tuesday in Los Angeles Superior Court differs from the model's papers that sought joint legal custody with visitation for Seal of Leni, 7½, Henry, 6½, Johan, 5, and Lou, 2.
But a source tells PEOPLE this is merely a legal technicality and no custody fight is expected. As with Klum's petition, Seal's papers cite the standard "irreconcilable differences" for the end of the nearly seven-year marriage.
Rumors first swirled that Klum, 38, and Seal, 49, were planning to divorce the day before they made the announcement.
For the couple who married in Mexico in 2005, the split played out in headlines as the end of a fairy tale as both Seal and Klum gradually stopped wearing their wedding rings.