Did Shakespeare write all his plays alone, and how do scholars tell who wrote which scene?

No. Shakespeare was a collaborator, and the evidence is in the style of the writing. Most playwrights of his period collaborated at some point, as critics agree Shakespeare did, mostly early and late in his career. The 36 plays of the First Folio are the core of the canon, but some are thought to be collaborations, and two further co-authored plays, Pericles and The Two Noble Kinsmen, are counted in the canon.

How can scholars tell? Attribution studies rest on the idea that every writer has a unique, measurable style. For Henry VIII, which was accepted as Shakespeare's alone until 1850, James Spedding noticed that some scenes were closer to the style of John Fletcher. He divided the play using eleven-syllable lines. In 1962 Cyrus Hoy divided it from word choices such as Fletcher's ye for you and 'em for them, and reached the same conclusions a century later. There is no contemporary document that proves the collaboration: the evidence lies in the style of the verse.

Another case is Timon of Athens: linguistic markers characteristic of Thomas Middleton cluster in certain scenes, and the evidence suggests he wrote about a third of the play. Some cases remain disputed: Pericles is judged a collaboration with George Wilkins by the Oxford and Arden editors, but the Cambridge editors say it is entirely Shakespeare's.