  Let GradAlg(H) be the scheme parameterizing graded quotients of
R=k[x_0,...,x_n] with Hilbert function H (it is a subscheme of the Hilbert
scheme of P^n if we restrict to quotients of positive dimension, see definition
below). A graded quotient A=R/I of codimension c is called standard
determinantal if the ideal I can be generated by the t by t minors of a
homogeneous t by (t+c-1) matrix (f_{ij}). Given integers a_0\le a_1\le ...\le
a_{t+c-2} and b_1\le ...\le b_t, we denote by W_s(\underline{b};\underline{a})
the stratum of GradAlg(H) of determinantal rings where f_{ij} \in R are
homogeneous of degrees a_j-b_i.
  In this paper we extend previous results on the dimension and codimension of
W_s(\underline{b};\underline{a}) in GradAlg(H) to {\it artinian determinantal
rings}, and we show that GradAlg(H) is generically smooth along
W_s(\underline{b};\underline{a}) under some assumptions. For zero and one
dimensional determinantal schemes we generalize earlier results on these
questions. As a consequence we get that the general element of a component W of
the Hilbert scheme of P^n is glicci provided W contains a standard
determinantal scheme satisfying some conditions. We also show how certain ghost
terms disappear under deformation while other ghost terms remain and are
present in the minimal resolution of a general element of GradAlg(H).
