  We present an exact diagonalization study of the single particle spectral
function in the 1D and 2D t-J model. By studying the scaling properties with J
and t we find a simple building pattern in 1D and show that every spectral
feature can be uniquely assigned by a spinon and holon momentum. We find two
types of low energy excitations: a band with energy scale J and high spectral
weight disperses upwards in the interior part of the Brillouin zone and reaches
E_F at k_F, and a band with energy scale t and low spectral weight disperses
downwards in the outer part of the zone, touching E_F at 3k_F. An analogous
analysis of the 2D case at half filling shows that the t-band exists also in
this case, but is diffuse and never reaches the Fermi energy. For the doped
case in 2D the picture is more reminiscent of 1D, in particular the `main-band'
with a dispersion proportional J and the `shadow band' with energy scale t can
be identified also in this case. This leads us to propose that the shadow bands
discovered by Aebi et al. in Bi2212 are the 2D analogue of the 3k_F singularity
in 1D systems and unrelated to antiferromagnetic spin fluctuations.
