Pictures
(v5, p56)
(v5, p64)
The following were notes while the character was evolving. They do not necessarily represent the way it came out.
Son of Aaronev, prince of Sturmhalten. Direct descendant of the "Storm King", Andronicus Valois, through his mother's side (v5, p83).
Tarvek looks much like his father, according to Lucrezia on (v5, p96).
Since his father's death, Tarvek is heir-presumptive to Sturmhalten, as he reminds Vrin on (v5, p96).
Tarvek plays both sides of the fence so well, it is [completely unclear] which side he is really on. If any -- his style seems to be deliberate ambiguity. Indeed, he [doesn't even entirely mind if that is known]: he just specializes in convincing all sides that he is really with them. There is [some reason to believe] that he is really aligned with Agatha, and is plotting with Moxana, but it's hard to be sure.
The one time we see Tarvek in a fairly unguarded moment seems to be [this page]. In this, he makes pretty clear that his personal priority is overthrowing Klaus and re-establishing himself as the Storm King; this rings pretty true. He clearly believes that this would be for the best for everyone, but he is also clearly susceptible to typical Sparky megalomania. Of course, he accidentally confesses this to Lucrezia, instead of Agatha as intended.