  The wetting transition of the Blume-Capel model is studied by a finite-size
scaling analysis of $L \times M$ lattices where competing boundary fields $\pm
H_1$ act on the first row or last row of the $L$ rows in the strip,
respectively. We show that using the appropriate anisotropic version of finite
size scaling, critical wetting in $d=2$ is equivalent to a "bulk" critical
phenomenon with exponents $\alpha =-1$, $\beta =0$, and $\gamma=3$. These
concepts are also verified for the Ising model. For the Blume-Capel model it is
found that the field strength $H_{1c} (T)$ where critical wetting occurs goes
to zero when the bulk second-order transition is approached, while $H_{1c}(T)$
stays nonzero in the region where in the bulk a first-order transition from the
ordered phase, with nonzero spontaneous magnetization, to the disordered phase
occurs. Interfaces between coexisting phases then show interfacial enrichment
of a layer of the disordered phase which exhibits in the second order case a
finite thickness only. A tentative discussion of the scaling behavior of the
wetting phase diagram near the tricritical point also is given.
