Neurosurgically grown neural link between two brains? I guess it's possible to surgically restore neural connection after a trauma (e.g. a severed hand can be reattached if done quickly).

And, from history of evolution of hominids, it seems that just by increasing brain size by 30% it's possible to develop a radically higher level of cognitive abilities. 

Putting these two ideas together, I wonder if anyone tried to grow a neural link between two separate brains. Maybe even a narrow, low-bandwidth wisp of neurons between two brains would adapt itself to expand the consciousness. I wonder what will be the effect of such a 100% increase in brain size. And if it works, we can connect three brains, then four, five, etc. Of course, these "compound people" would have trouble moving around as they won't be able to separate their heads more than few centimeters...but if the tradeoff is that they become exponentially more sentient...? 

Could you please point to some research performed in this direction? 
Is it even legal in developed countries? Thank you.
Research exists on craniopagus twins, maybe most notably Tatiana and Krista, who seem to share sensory input somewhat. I doubt that connective mechanisms such as this abnormal case would suffice to permit "compound cognition" in ways that would enhance cognitive ability similarly to your point about hominid evolution. Your relatively simple proposal for a connective cord of neurons strikes me as roughly equivalent, though more complex connections may not be entirely unfeasible in the long run.

Before I move on to speculating about that, consider a few other points from cognitive neuroscience thus far. Plenty of split-brain research (on people and animals with dysfunctional corpus callosums) exists as well, little of which shows what I would call "radical effects on cognitive abilities". Results are somewhat more subtle than that: e.g., involving object recognition more than what laypeople would recognize as intelligence, especially social communication and basic reasoning, which remain relatively intact. You might also be surprised at the modest effects of losing an entire cerebral hemisphere: again, it's not what I would call a 50% reduction in cognitive ability, at least as we understand and use such abilities in modern social contexts.

Non-biological methods are already being experimented with for brain-to-computer and even human brain-to-brain interfacing (Armstrong &amp; Ma, 2013), but we're some distance away from really augmenting cognitive abilities through such methods in the way evolution seems to have augmented them in hominids. Consider also that evolution seems to have proceeded in far more complex manners than those by which we're connecting brains now. Changes occurring organically throughout the brain over millions of years of natural selection may have developed our cognitive abilities well beyond those of smaller-brained animals, but these changes have probably been much more sophisticated than simply wiring disparate parts together, let alone only one part to only one other. Cognitive processes are functionally dispersed broadly across our incredibly complex neural structures; we definitely use more than 10% of our brains. There's really no particularly promising hub-of-all-cognitive-ability through which one could connect and expect to provide consciousness-wide augmentation (that I know of), nor would it be as simple as connecting one brain to another.

To throw in a halfhearted computer metaphor, consider how little processing ability is gained simply by connecting two computers by LAN cable. In very many ways, computer processing augmentation has had to proceed much more incrementally, component by component. Multi-core processors and several sticks of RAM per computer are commonplace now, but to truly augment computing performance with these, fundamental architectural changes in connective design have necessarily occurred. Far more than one wire connects these compound components.

Thinking in this manner might pave the way to future innovations that may someday achieve the effects you have in mind. Transhuman cognitive augmentation research is rapidly advancing in very many directions, some of which may bear satisfying similarities to your idea. They're all well beyond the scope of my knowledge or of this answer though, so I'll just toss some Wikipedia links at you to get things started. Please feel welcome to ask separate questions to follow up on cyberpsychological topics; I find them all very exciting, and would be very eager to explore them further with you and our community! 


Intelligence amplification
Cyborgs, cybernetics, and cyberware


Exocortex – artificial external augmentation system for high-level cognitive processes
Neuroprosthetics – devices to substitute motor, sensory, or cognitive modalities


Visual prosthetics


Artificial brains


The Blue Brain Project – a molecular reverse-engineering of the mammalian brain
Artificial intelligence – arguably more on-topic at the dedicated AI Stack Exchange


Hierarchical temporal memory – online machine learning structural neocortical model

Wetware computers – built from organic, living neurons!

Nootropics – cognition, memory, intelligence, motivation, attention, and concentration drugs


See a related question, Do smart drugs (nootropics) make you smarter?
Ampakines – compounds that enhance attention span, alertness, learning, and memory

Transcranial direct-current stimulation


See a related question, Can learning be facilitated by transcranial magnetic stimulation?

Mind uploading – copying mental content from a brain substrate to another computational device


Depends on brain reading / fingerprinting / thought identification

Augmented reality


Consumer brain-computer interface devices
Neurofeedback – illustration of brain activity to teach self-regulation
Augmented learning – adaptive learning environments
Electronic learning
Web-based simulation
Wearable computers


Head-up displays – transparent data displays that accommodate users' usual viewpoints


Bionic contact lenses and virtual retinal displays
Optical head-mounted displays
EyeTap
Google Glass





Reference


Armstrong, D., &amp; Ma, M. (2013, August 27). Researcher controls colleague’s motions in 1st human brain-to-brain interface. Washington University: News and Information. Retrieved from http://www.washington.edu/news/2013/08/27/researcher-controls-colleagues-motions-in-1st-human-brain-to-brain-interface/.