  We show that for any finite generic union of pairs $(x_i,L_i)_i$ where
$x_i\in L_i$ is a point of the line $L_i$ in projective $n$-space, the divisors
$m_ix_i$ on the $L_i$ have maximal rank with respect to homogeneous $d$ forms
for all $d\geq 0$ and all $m_i\geq 0$ modulo the expected numerical
restrictions.
