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We study $c$-crossing-critical graphs, which are the minimal graphs thatrequire at least $c$ edge-crossings when drawn in the plane. For every fixedpair of integers with $c\ge 13$ and $d\ge 1$, we give first explicitconstructions of $c$-crossing-critical graphs containing a vertex of degreegreater than $d$. We also show that such unbounded degree constructions do notexist for $c\le 12$, precisely, that there exists a constant $D$ such thatevery $c$-crossing-critical graph with $c\le 12$ has maximum degree at most$D$. Hence, the bounded maximum degree conjecture of $c$-crossing-criticalgraphs, which was generally disproved in 2010 by Dvo\v{r}\'ak and Mohar(without an explicit construction), holds true, surprisingly, exactly for thevalues $c\le 12.$

Bounded maximum degree conjecture holds precisely for $c$-crossing-critical graphs with $c \leq 12$