  Proca stars are self-gravitating Bose-Einstein condensates obtained as
numerical stationary solutions of the Einstein-(complex)-Proca system. These
solitonic can be both stable and form dynamically from generic initial data by
the mechanism of gravitational cooling. In this paper we further explore the
dynamical properties of these solitonic objects by performing both head-on
collisions and orbital mergers of equal mass Proca stars, using fully
non-linear numerical evolutions. For the head-on collisions, we show that the
end point and the gravitational waveform from these collisions depends on the
compactness of the Proca star. Proca stars with sufficiently small compactness
collide leaving a stable Proca star remnant. But more compact Proca stars
collide to form a transient ${\it hypermassive}$ Proca star, which ends up
decaying into a black hole, albeit temporarily surrounded by Proca quasi-bound
states. The unstable intermediate stage can leave an imprint in the waveform,
making it distinct from that of a head-on collision of black holes. The final
quasi-normal ringing matches that of Schwarzschild black hole, even though
small deviations may occur, as a signature of sufficiently non-linear and
long-lived Proca quasi-bound states. For the orbital mergers, the outcome also
depends on the compactness of the stars. For most compact stars, the binary
merger forms a Kerr black hole which retains part of the initial orbital
angular momentum, being surrounded by a transient Proca field remnant; in cases
with lower compactness, the binary merger forms a massive Proca star with
angular momentum, but out of equilibrium. As in previous studies of (scalar)
boson stars, the angular momentum of such objects appears to converge to zero
as a final equilibrium state is approached.
