I don't get you. How do you get that 50% figure of State ?
Till 14th Finance commission states were getting 32% and after 14th commission states share is raised to 42% from central tax pool. It means now states has more financial autonomy from earlier position. States have now 10% more funds to spend as per their wish.
Now earlier social welfare projects were mostly funded (75%)by center as States were eligible for only 32% monetary value so they bear earlier PM names but now as center has raised the States monetary share in 14th commission so center has reduced their monetary share in social welfare projects from 75% to 50%. And that's why we see many central projects are renamed again before implementing in States.
I can give you Bengal's data. For example central Swatchha Bharat or Beti bachao mission beti parao (girl child education) does not exists here, our TMC govt renamed those projects as Nirmal bangla and KanyaShri etc projects.
Anything wrong in my data ?