  The family of complex projective surfaces in projective three space of degree
$d$ having precisely $\delta$ nodes as their only singularities has codimension
$\delta$ in the linear system of surfaces of degree $d$ for sufficiently large
$d$ and is of degree
$N_{\delta,complex}(d)=(4(d-1)^3)^\delta/\delta!+O(d^{3\delta-3})$. In
particular, this number is polynomial in $d$.
  By means of tropical geometry, we explicitly describe
$(4d^3)^\delta/\delta!+O(d^{3\delta-1})$ surfaces passing through a suitable
generic configuration of $n=\binom{d+3}{3}-\delta-1$ points in projective three
space. These surfaces are close to tropical limits which we characterize
combinatorially, introducing the concept of floor plans for multinodal tropical
surfaces. The concept of floor plans is similar to the well-known floor
diagrams (a combinatorial tool for tropical curve counts): with it, we keep the
combinatorial essentials of a multinodal tropical surface which are sufficient
to reconstruct the surface.
  In the real case, we estimate the range for possible numbers of real
multi-nodal surfaces satisfying point conditions. We show that, for a special
configuration $w$ of real points, the number $N_{\delta,real}(d,w)$ of real
surfaces of degree $d$ having $\delta$ real nodes and passing through $w$ is
bounded from below by $(\frac{3}{2}d^3)^\delta/\delta! +O(d^{3\delta-1})$.
  We prove analogous statements for counts of multinodal surfaces in $P^1\times
P^2$ and $P^1\times P^1\times P^1$.
