  We investigate the ground state of a (1+1)-dimensional conformal field theory
built with $M$ species of massless free Dirac fermions coupled at one boundary
point via a conformal junction/interface. Each CFT represents a wire of finite
length $L$. We develop a systematic strategy to compute the R\'enyi entropies
for a generic bipartition between the wires and the entanglement negativity
between two non-complementary sets of wires. Both these entanglement measures
turn out to grow logarithmically with $L$ with an exactly calculated universal
prefactor depending on the details of the junction and of the bipartition.
These analytic predictions are tested numerically for junctions of free Fermi
gases, finding perfect agreement.
