Immigration documents

Hi, hope this question is appropriate for this forum. I've been researching my grandparent's immigration to the US from eastern Europe. I know the dates and ports of entry for their arrival (based on ship passenger manifests), as well as where they were born; but I was wondering if immigrants arriving in the early 1900s (around 1908-1912) were required to have any type of passport or similar documents from their country of origin? Or did they just buy a ticket on a steamship and show up here? Thank you, joan stachnik