How to predict shares? Lets say I know what is the overall budget for some units and I want to predict share of budget each unit will get. I have historical data and could do regression analysis. Is it better to predict shares directly with logistic regression or to try to predict amount and then get calculate its share in overall predictions? Or something else? One more thing, I would like to spread entire budget at the end.
 A: Political scientists deal with a similar problem when analyzing multiparty election data. One convenient way to estimate such models is via SURE (Seemingly Unrelated REgressions). See articles here http://pan.oxfordjournals.org/content/10/1.toc for details.
A: There are two questions here.  1) Whether it is better to model unit-specific amounts or unit-specific shares.  2) Whether the fact that there is a budget constraint means that one cannot treat the unit-specific amounts/shares as independent. 
1) The answer here depends a lot on what the data looks like and what question you want to answer.  I think modeling amounts is likely to be easier, since you cannot run canned logistic regression procedures if your data range from 0 to 1 instead of being equal to 0 or 1.  One other thing to worry about is whether there any zero amounts/shares.  If there are, this will constrain your modeling choices a lot.
2) Regardless of whether you model share or amount, there is a potential problem with non-independence of your observations.  The simplest option is to model the amount each unit received, ignoring the fact that the unit-specific amounts were constrained to add up to the total of the budget.  This assumes that the errors in prediction for each unit are uncorrelated, which is not true if there is really a total budget constraint. The budget constraint implies a negative correlation of errors. 
Whether or not ignoring the budget constraint is a reasonable approximation depends on how many units you have in the data.  If there are only a couple units, then ignoring the constraint is potentially problematic, because there is a large negative correlation in the error terms for each unit's share of the budget.  In the extreme case of two units, a budget constraint implies that the correlation between the errors of the two units is -1.
But if you have many units (I would say anything over about 15 is enough, but this is a judgment call) than your analysis will likely have more serious problems than the fact that you have ignored a small amount of negative correlation among the errors!
