What happen after seven southern states seceded from the union?

When South Carolina became the first state to secede from the Union, they were breaking all ties to the United States and forming their own government. They did not secede until after the 1860 election and inauguration of Abraham Lincoln as president of the United States. They had supported the democratic candidate for president, but he lost to Lincoln. They were afraid Lincoln was going to abolish slavery and waited until he was actually president before trying to leave the Union. By cutting ties to the U. S., they effectively nullifed the results of the 1860 election and the Confederate states chose Jefferson Davis as their president. However, Lincoln and Congress never recognized their rights to leave the Union and that's why the Civil War began.