How far can a signal travel in the neocortex without passing through the white matter? Correct me if I am wrong please, from what I understand horizontal communication spans very short distance in all layers of the neocortex but layers I and II. In these two layers dendrites and axons can travel horizontally a little farther, but how far? Also the question can have different subcases. First one, how far can one single dendrite or axon travel horizontally in the neocortex ? Second one, how far can a signal travel (possibly going through several synapses) horizontally in the neocortex?
The distance of horizontal communication depends on species, cortical region, and cortical layer. Very few combinations of those 3 factors have ever been studied. For the combinations with which I am familiar, most horizontal connections are limited to a few hundred microns, though some are as long as a few millimeters. Most of that distance is axonal because dendrites are generally much shorter than axons. Of all the connections I've read about, none span an entire region. To get across a region, a connected series of signals would have to make several hops through several neurons and across several synapses, as you suggested in your question.

The direct path of an axon connecting two cortical areas (or an axon from a subcortical area to a cortical area) is through the white matter, but sometimes an axon will additionally ascend to layer I of the target area before branching, presumably to save space. This is the main use of layer I, and the lengths of these connections is several millimeters or centimeters.

I have never heard of the longer-distance horizontal connections that you suggest occur in layer II; layers II through VI contain neurons with short horizontal and vertical connections.

References


  
  Alonso, J.-M. (2002) Neural Connections and Receptive Field Properties in the Primary Visual Cortex. The Neuroscientist. 8(5): 443-456.
  Feldmeyer, D. (2012) Excitatory Neuronal Connectivity in the Barrel Cortex. Frontiers in Neuroanatomy. 6: 1-22.
  Rockland, K.S. and Virga, A. (1989) Terminal Arbors of Individual Feedback Axons Projecting from Area V2 to V1 in the Macaque Monkey: A Study Using Immunohistochemistry of Anterogradely Transported Phaseolus vulgaris-leucoagglutinin. The Journal of Comparative Neurology. 285: 54-72.