Adjusting for baseline differences in growth models

Hi all, I posted a long question for this the other day, but no one
has responded.  Here is a short version those of you who are very busy
might have time to read.  Any advice would be greatly appreciated.

I have a growth model where 2 groups differ on the outcome at
baseline.  How do I get the growth model adjusting for this difference
(or making the groups equivalent at baseline, such as in ANCOVA)?
Predict growth from a 2nd(person)-level covariate of baseline scores
(i.e., a growth:baseline covariate interaction in a mixed model)?
Does it make sense to add the baseline covariate as a predictor of the
intercepts as well as the slopes or is this completely redundant with
a model where time is coded so that 0 = baseline?

Thanks again.

- DC