  In this paper, we study the newly discovered universal splitting behavior for
tree-level scattering amplitudes of particles and strings~\cite{Cao:2024gln}:
when a set of Mandelstam variables (and Lorentz products involving
polarizations for gluons/gravitons) vanish, the $n$-point amplitude factorizes
as the product of two lower-point {\it currents} with $n{+}3$ external legs in
total. We refer to any such subspace of the kinematic space of $n$ massless
momenta as ``2-split kinematics", where the scattering potential for string
amplitudes and the corresponding scattering equations for particle amplitudes
nicely split into two parts. Based on these, we provide a systematic and
detailed study of the splitting behavior for essentially all ingredients which
appear as integrands for open- and closed-string amplitudes as well as
Cachazo-He-Yuan (CHY) formulas, including Parke-Taylor factors, correlators in
superstring and bosonic string theories, and CHY integrands for a variety of
amplitudes of scalars, gluons and gravitons. These results then immediately
lead to the splitting behavior of string and particle amplitudes in a wide
range of theories, including bi-adjoint $\phi^3$ (with string extension known
as $Z$ and $J$ integrals), non-linear sigma model, Dirac-Born-Infeld, the
special Galileon, \textit{etc.}, as well as Yang-Mills and Einstein gravity
(with bosonic and superstring extensions). Our results imply and extend some
other factorization behavior of tree amplitudes considered recently, including
smooth splittings~\cite{Cachazo:2021wsz} and factorizations near
zeros~\cite{Arkani-Hamed:2023swr}, to all these theories. A special case of
splitting also yields soft theorems for gluons/gravitons as well as analogous
soft behavior for Goldstone particles near their Adler zeros.
