Look like you know a lot about morphology , to me Balcsika drawing don't look so different from the one I've seem at the side of it's fossil head in a museum, just a little bulkier. 
So... maybe you find it silly but I can't understand why Livyatan Melvillei was closer to a sperm whale if it resemble more a killer whale(I guess)
. Can you help me with this question?
So... maybe you find it silly but I can't understand why Livyatan Melvillei was closer to a sperm whale if it resemble more a killer whale(I guess)
. Can you help me with this question? 
To undertstand the relations of Livyatan with other whales, it´s good to take a look at this phylogenetic tree:
de.wikipedia.org/wiki/Livyatan…
Modern sperm whales are among the most specialized of all whales, and they have a lot of weird anatomical traits, like giant size, (usually) non-erupting upper teeth, a giant spermaceti organ which covers the whole rostrum, multiple "humps", wrinkled skin (it´s not always wrinkled BTW), a fully anterior and lateral blowhole and several other things. But in the past, there were much more kinds of sperm whales, which were similar in some anatomical traits to modern sperm whales, but still very different in others. For example, the ancestral sperm whales were not giants, but ranged from the size of a big dolphin to a big orca. They had still upper teeth, and their skulls show that in some very early lines, the spermaceti organ was still not covering the whole snout (like in Zygophyseter for example). Some of those very early sperm whales were probably just fish-eaters with comparably thin rounded teeth, but several lines evolved a more predatory way of live with massive interlocking teeth with sharp shearing edges, for example Brygmophyseter, Zygophyseter and Hoplocetus ritzi, which were probably very similar in ecology to modern orcas (which have also a very wide range of different prey animals), other were quite small but had massive jaws and teeth like Acrophyseter. The line which did lead to Livyatan was also different. It was still closer to modern sperm whales than the forementioned species, but still not as close to modern sperm whales as pygmy sperm whales are to Physeter catodon. After all, Livyatan was totally unique, and in its anatomical traits to some degree just parallel evolutions to both killer whales and modern sperm whales, but based on the bauplan of archaic sperm whales. It´s all somewhat complex and not that easy to explain.
The problem with the life-reconstruction in the museum it that it includes some errors too.
de.wikipedia.org/wiki/Livyatan…
Modern sperm whales are among the most specialized of all whales, and they have a lot of weird anatomical traits, like giant size, (usually) non-erupting upper teeth, a giant spermaceti organ which covers the whole rostrum, multiple "humps", wrinkled skin (it´s not always wrinkled BTW), a fully anterior and lateral blowhole and several other things. But in the past, there were much more kinds of sperm whales, which were similar in some anatomical traits to modern sperm whales, but still very different in others. For example, the ancestral sperm whales were not giants, but ranged from the size of a big dolphin to a big orca. They had still upper teeth, and their skulls show that in some very early lines, the spermaceti organ was still not covering the whole snout (like in Zygophyseter for example). Some of those very early sperm whales were probably just fish-eaters with comparably thin rounded teeth, but several lines evolved a more predatory way of live with massive interlocking teeth with sharp shearing edges, for example Brygmophyseter, Zygophyseter and Hoplocetus ritzi, which were probably very similar in ecology to modern orcas (which have also a very wide range of different prey animals), other were quite small but had massive jaws and teeth like Acrophyseter. The line which did lead to Livyatan was also different. It was still closer to modern sperm whales than the forementioned species, but still not as close to modern sperm whales as pygmy sperm whales are to Physeter catodon. After all, Livyatan was totally unique, and in its anatomical traits to some degree just parallel evolutions to both killer whales and modern sperm whales, but based on the bauplan of archaic sperm whales. It´s all somewhat complex and not that easy to explain.
The problem with the life-reconstruction in the museum it that it includes some errors too.