Can random deposition create dense non-overlapping material feeding? The question is very fundamental for the research of particle packing, while the answer is of great importance for any industrial process that applies single object operation. To gain an insight into this issue, we studied the overlap problems of convex particles in the manner of uniformly random deposition. The overlap probability of two convex particles with arbitrary shapes and sizes is formulated, and the coverage fractions of free particles and sticking particles (particles of the bottom layer) are precisely predicted. Simulations with rectangular particles verified the theory. Surprisingly, free particles can only occupy less than 7.5% of the plane area, much smaller than what is intuitively expected. Sticking particles, however, can easily cover 19%, a factor of 2.5 times larger. The finding is of great value for applications that need to create dense non-overlapping feeding.