Yes, there are still several stallions syndicated these days. Ofcourse, the larger farms such as Juddmonte do not syndicate, but I believe that Darley have begun to syndicate - definitley in the southern hemisphere.
Shareholders do ofcourse recieve shareholder nominations to the horse, which they can either use or sell themselves. Depending on the agreement, shareholders are often given two nominations in the first few years to help get him off and running - and then one nom each year after.
Dividends are payable to shareholders, but for these to be payable the stallion must cover enough mares for both the stud allocation and the shareholding allocation for there to be 'overs'.