On splitting trees

We investigate two variants of splitting tree forcing, their ideals and regularity properties. We prove connections with other well-known notions, such as Lebesgue measurablility, Baire- and Doughnut-property and the Marczewski field. Moreover, we prove that any absolute amoeba forcing for splitting trees necessarily adds a dominating real, providing more support to Hein's and Spinas' conjecture that (Formula presented.).