  In this note we consider a multi-slit Loewner equation with constant
coefficients that describes the growth of multiple SLE curves connecting $N$
points on $\mathbb{R}$ to infinity within the upper half-plane. For every
$N\in\mathbb{N}$, this equation provides a measure valued process $t\mapsto
\{\alpha_{N,t}\},$ and we are interested in the limit behaviour as
$N\to\infty.$ We prove tightness of the sequence
$\{\alpha_{N,t}\}_{N\in\mathbb{N}}$ under certain assumptions and address some
further problems.
