  Let $\nu$ be a valuation of arbitrary rank on the polynomial ring $K[x]$ with
coefficients in a field $K$. We prove comparison theorems between
MacLane-Vaqui\'e key polynomials for valuations $\mu\le\nu$ and abstract key
polynomials for $\nu$.
  Also, some results on invariants attached to limit key polynomials are
obtained. In particular, if $\operatorname{char}(K)=0$ we show that all limit
key polynomials of unbounded continuous MacLane chains have numerical character
equal to one.
